Winamp & SHOUTcast Forums Mathematical Logic [part 2]

 27th March 2003, 01:17 #321 anubis2003 Forum King     Join Date: Dec 2002 Location: middle of somewhere Posts: 5,564 Well, I would teach them algebra, but that doesn't fit into your rules. Anyone else know? I am really curious to see what the answer is. [Over The Monkey] | [My DeviantArt] | [Seti] | [Atmo Digital Design Forums]
 27th March 2003, 01:22 #322 ujay Forum King     Join Date: Jul 2001 Location: London Posts: 6,074 The number of heads is the number of animals. Suppose it was 13 hens then there is an excess of 14 legs, which means we have 7 lots of 2 legs with which we can 'upgrade' 7 of the hens to goats, So there are 7 goats and (13-7) =6 hens. UJ
 27th March 2003, 01:24 #323 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 can a 7 year old count to 40?
 27th March 2003, 01:35 #324 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Let me rephrase the question, so that we may quickly end this (the original one is ambiguous - depending on how you interpret it, 50/50 could be correct): You come up to a couple, and find out that they have two children. You ask, "Is one of those children a girl?". They respond, "yes". What is the likelihood of the other child being a boy? Note: If someone doesn't explain this correctly by tomorrow, I will. Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 27th March 2003, 01:55 #325 anubis2003 Forum King     Join Date: Dec 2002 Location: middle of somewhere Posts: 5,564 50/50. The sex of the other child is independent of the fact that one is a girl. [Over The Monkey] | [My DeviantArt] | [Seti] | [Atmo Digital Design Forums]
27th March 2003, 01:56   #326
Rumata
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Quote:
 Originally posted by ujay The number of heads is the number of animals. Suppose it was 13 hens then there is an excess of 14 legs, which means we have 7 lots of 2 legs with which we can 'upgrade' 7 of the hens to goats, So there are 7 goats and (13-7) =6 hens. UJ

This how it was explained to me when I was 7. Imagine that the goats started walking on their hind legs and using their front legs as arms. Then there would be twice as many legs as there are heads. 26 legs. That leaves us with 14 former legs that became arms. There are 2 arms per goat so there are 7 goats. That leaves 6 heads that are chickens. I had so much fun imagining goats walking on their hind legs that I still remember it 20 years later.

 27th March 2003, 02:27 #327 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 rumata, nice. that is a very interesting method. neverthought of it that way.
 27th March 2003, 02:45 #328 anubis2003 Forum King     Join Date: Dec 2002 Location: middle of somewhere Posts: 5,564 Me is confused - Goats walking on two legs??? JK, but that way seems really weird to me. I just like the algebra approach - short and sweet. [Over The Monkey] | [My DeviantArt] | [Seti] | [Atmo Digital Design Forums]
 27th March 2003, 18:31 #329 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Phhff. The approach is basically the same. goats = (legs-(heads * 2))/2 and of course, hens = heads - goats Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 27th March 2003, 23:50 #330 zootm Forum King     Join Date: Jan 2002 Location: the nether reaches of bonnie scotland Posts: 13,375 i have a correct answer to this from when i was doing a probabilities course. i just really can't be bothered finding it. i remember some of the things.
28th March 2003, 00:01   #331
Rumata
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Quote:
 Originally posted by xzxzzx Phhff. The approach is basically the same. goats = (legs-(heads * 2))/2 and of course, hens = heads - goats
The challenge was not to provide an algebraic solution. Any 8-th grader can do that. The challenge was to come up with purely arithmetic line of reasoning. Like what ujay did.

 28th March 2003, 01:10 #332 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 The point is that it is the same solution. Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 28th March 2003, 01:24 #333 Rumata Junior Member   Join Date: Mar 2003 Posts: 11 Well duh. Of course it's the same solution. Would be strange if this trivial problem were to demonstrate an incosistency between different branches of mathematics.
 28th March 2003, 01:28 #334 anubis2003 Forum King     Join Date: Dec 2002 Location: middle of somewhere Posts: 5,564 That would be cool, but would require going into advanced mathematics to get something that would disagree. [Over The Monkey] | [My DeviantArt] | [Seti] | [Atmo Digital Design Forums]
 28th March 2003, 01:40 #335 ujay Forum King     Join Date: Jul 2001 Location: London Posts: 6,074 The answers are the same it's true, they must be, but goats = (legs-(heads * 2))/2 is too compact and abstract for a 7 year old. The whole thing can be turned around to give the following solutions (i) If all the animals were goats there would be 12 legs too many, so six of the goats have to lift their front legs in the air and pretend they are hens. If there are 6 hens there must be 7 goats. (ii) hens = ((heads*4)-legs)/2 You have to admit the first is easier for a 7 year old to understand, even though the second says exactly the same as the first. Move on Someone post a riddle then. UJ
1st April 2003, 08:16   #336
xzxzzx
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Well, looks like it's time for me to remind everyone that this thread exists.

Here's the "riddle"
Quote:
 You come up to a couple, and find out that they have two children. You ask, "Is one of those children a girl?". They respond, "yes". What is the likelihood of the other child being a boy?
Ok, here's the explanation (if you disagree, please point out exactly what step is wrong is this logical progression):
1. The equally possible children of the couples that you would meet (let's ignore biological reasons, and assume the chances between a boy and a girl are 50%) would be the following four: GG BG GB BB
2. Therefore, we can find the four equally probable results to the question "Is one of those children a girl?", which are Yes, Yes, Yes, and No.
3. Of the 3 "yes" answers, two of the pairs of children have a boy.
4. Therefore, there is a 2 in 3, or (roughly) 66% chance that the other child is a boy.

Of course, by "one child", we mean we don't care what sex the other is. Otherwise, it's a 100% chance.

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 1st April 2003, 12:38 #337 mindlessjackal Junior Member   Join Date: Apr 2003 Posts: 5 depends on the form of the question and its interpretation. http://mathforum.org/dr.math/faq/faq...rl.choose.html however the basic logic if choosing the family first is correct
 1st April 2003, 17:28 #338 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Um... The question was explicitly stated, and the form of it's collection, too. Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 1st April 2003, 17:35 #339 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 the likely hood of him being a boy is 49.5%. 49.5% chance its a boy, 49.5% chance it's a girl, and 1% chance its a hermaphrodite. (I mean, it either is a boy or it isnt,or it could be both.)
 1st April 2003, 18:27 #340 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 what if its a salmon? theyc an change their sex.
1st April 2003, 20:38   #341
xzxzzx
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Quote:
 Originally posted by SSJ4_Gogitta 49.5% chance its a boy, 49.5% chance it's a girl, and 1% chance its a hermaphrodite.
And here's why we should assume 50/50 for one boy/girl.
However, following your logic, it would mean at least a 50.5%, because a hermaphrodite would be a boy AND a girl, would it not?

Let's see. If we took that into account...

I calculate it at 67.5452829564% (roughly)

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 1st April 2003, 20:41 #342 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Hey-Hey! I'm a "Major Dude"... (I just noticed this) Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 1st April 2003, 21:24 #343 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 if it is either a boy, or a girl (no mix) then there is a 50% chance of either. Because it either is, or it isnt a boy, only 2 choices. Btw, i was being silly with the hermaphrodite.
 1st April 2003, 21:46 #344 CremoNe Senior Member     Join Date: Feb 2002 Location: Italy Posts: 397 what is the question. [size=0.1]The Durango 95 purred away real horrorshow, a nice warm vibratey feeling all through your guttiwuts[/size]
1st April 2003, 22:12   #345
xzxzzx
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Quote:
 Originally posted by SSJ4_Gogitta if it is either a boy, or a girl (no mix) then there is a 50% chance of either. Because it either is, or it isnt a boy, only 2 choices. Btw, i was being silly with the hermaphrodite.
So explain what part of the above logic has a flaw.

As for the hermaphrodite, um, DUH.

CremoNe: Go up 8 posts for the question.

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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1st April 2003, 22:56   #346
CremoNe
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Quote:
 Originally posted by xzxzzx Well, looks like it's time for me to remind everyone that this thread exists. Here's the "riddle" Ok, here's the explanation (if you disagree, please point out exactly what step is wrong is this logical progression): The equally possible children of the couples that you would meet (let's ignore biological reasons, and assume the chances between a boy and a girl are 50%) would be the following four: GG BG GB BB Therefore, we can find the four equally probable results to the question "Is one of those children a girl?", which are Yes, Yes, Yes, and No. Of the 3 "yes" answers, two of the pairs of children have a boy. Therefore, there is a 2 in 3, or (roughly) 66% chance that the other child is a boy.

[size=0.1]The Durango 95 purred away real horrorshow, a nice warm vibratey feeling all through your guttiwuts[/size]

 1st April 2003, 23:17 #347 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 BG and GB are the same. Think of it in terms of money. G = 0 cents B = 1 cent GG BG GB BB / 00 10 01 11 the BG GB both equate to 1 cent, and thus cancel each other out. "Of the 3 "yes" answers, two of the pairs of children have a boy." I can easly say that for the girl too. GG BG GB BB = 3 girls,1 boy GG BG GB BB = 3 boys, 1 girl 50/50
1st April 2003, 23:47   #348
Rumata
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Quote:
 Originally posted by xzxzzx Well, looks like it's time for me to remind everyone that this thread exists. Here's the "riddle" Ok, here's the explanation (if you disagree, please point out exactly what step is wrong is this logical progression):
Quote:
 The equally possible children of the couples that you would meet (let's ignore biological reasons, and assume the chances between a boy and a girl are 50%) would be the following four: GG BG GB BB Therefore, we can find the four equally probable results to the question "Is one of those children a girl?", which are Yes, Yes, Yes, and No.
1. WRONG. it's Yes, No, Yes, No
Quote:
 Of the 3 "yes" answers, two of the pairs of children have a boy. Therefore, there is a 2 in 3, or (roughly) 66% chance that the other child is a boy.
Of the TWO possible Yes answers, ONE has the second child as a boy and ONE has the second child as a girl. 50/50.

2nd April 2003, 01:48   #349
xzxzzx
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Clearly, you are all just not intelligent enough. Just kidding.

Ok, let's try and look at this another way.
1. The four equally probable families are the following:
GG GB BG BB
BG and GB are not the same, as they are equally likely situations. If you ignore order, you would have to qualify the likelihood:
25% - GG
50% - BG
25% - BB
2. Therefore, let's show what will happen in the four cases:
code:
a]GG: The answer will be "Yes", and the other child is a girl
b]BG: The answer will be "Yes", and the other child is a boy
c]GB: The answer will be "Yes", and the other child is a boy
d]BB: The answer will be "No"

3. And therefore, out of the three couples that would say "Yes", two of them will have a boy as the other child.
Quote:
 BG and GB are the same. Think of it in terms of money. G = 0 cents B = 1 cent GG BG GB BB / 00 10 01 11 the BG GB both equate to 1 cent, and thus cancel each other out.
That's an interesting way to look at it. However, in both cases where there is only one cent, the other 'coin' is 0.

Quote:
 WRONG. it's Yes, No, Yes, No
Huh? You mean BG doesn't have a girl in it?

Ok. That's basically the same argument (hopefully clarified), but it is the correct argument. If someone still disagrees, point out what's wrong.

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 2nd April 2003, 03:05 #350 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 what is wrong: Mathematicians are idiots (ok, they ain't, but in this case they are ). Strictly biologically speaking, the sex of an individual is completely independent of their siblings' sex. They are either a boy or a girl (assuming the baby is normal and healthy, and all that extra stuff . Therefore, the likelihood is 50/50. Math has no place in biology. 50/50 is the answer. I rest my case /edit: ok, i just repeats what Rumata said....sry. /further edit: An example that is most likely a waste of my time: I flip a coin. What are the odds I get 'heads'? 50/50 right? I flip it again. Why should the odds of that flip be any different? Has a side been added? (no, it will not land on it's rim ) no. It's options are still heads and tails. The odds remain 50/50.
 2nd April 2003, 03:50 #351 mindlessjackal Junior Member   Join Date: Apr 2003 Posts: 5 another way of doing this not using sample spaces is with a probability tree code: First Second Unconditional Child Child Probability __G(1/2)__ 1/4 | __G(1/2)__| | |__B(1/2)__ 1/4 | Family -| | __G(1/2)__ 1/4 |__B(1/2)__| | |__B(1/2)__ 1/4 this shows that the probability of having a boy and a girl, regardless of the order of birth/selection, is 1/4+1/4=1/2. however, this only is true because there are two different paths to this result- boy first, girl second and girl first, boy second now to the actual question. we know that out of 2 children, 1 is a girl, and we want to find the probability that the other is a boy. What we have now is a conditional probability, the probability tree now looks like this. code: First Second Unconditional Conditional Child Child Probability Probability __G(1/2)__ 1/4 1/3 | __G(1/2)__| | |__B(1/2)__ 1/4 1/3 | Family -| | __G(1/2)__ 1/4 1/3 |__B(1/2)__| This is because we know BB is not possible. Thefore there are 3 possibilities, 2 of which can be a boy. the probability of a boy given that there is a girl is: P(B|G)=1/3 + 1/3 = 2/3 checkout this for more info: http://mathforum.org/dr.math/faq/faq.boy.girl.html This is similar to flipping coins. The chance of heads or tails is always 50% - ie every time u flip there is a 50 % chance of u getting heads or tails. However if out of 2 flips, (at least)one of them is a head, the other one is 2/3 likely to be tails and 1/3 likely to be heads. Its a bit freaky, but its because you don't know which flip the head came up on. If I tell you that my first flip is a head, then it is a 50/50 chance, because u know that the tails-head and tails-tails options are gone.
 2nd April 2003, 03:51 #352 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 ok ok, i agree that there can be two answers.
 2nd April 2003, 04:02 #353 mindlessjackal Junior Member   Join Date: Apr 2003 Posts: 5 hehe dlinkwit27, you used the same example as me, but with a different explanation! You are right, if u flip, get a head, the next time is just as likely to be heads or tails However, if u flip twice, and tell me that one is a head - u could have flipped HH, HT, TH - this is different than the other situation as there is an extra possibility which increases the chances of tails , flipping tails on the first go, and heads on the second. This comparison is the same as whether u ask if one is a girl, or if the oldest is a girl. Trust me, statistics is not logical.
 2nd April 2003, 04:21 #354 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 The chance of flipping a coin and it landing on the rim is 1 in a trillion.
2nd April 2003, 06:51   #355
xzxzzx
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Biology has nothing to do with it. The other child is already born, and we are assuming 50/50 anyway.

Statistics is totally correct and logical (in this case, anyway).

Quote:
 Originally posted by dlinkwit27 ok ok, i agree that there can be two answers.
There is one correct answer to my question. If you re-word it, then there can be another answer. However, to my question, there is one, and only one correct answer - if you don't think it's right, then maybe this will:.

Try it. Flip two coins several times. Check how many times you get HT or TH, as opposed to HH. You'll find it's more. About 2/3s of the time, you will get TH or HT, and the rest, HH. (This is ignoring any times that you get TT, which, of course, wouldn't count towards anything). Really, try it!

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 2nd April 2003, 18:13 #356 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 One coin is already flipped. you cant just change the sex of the girl at will. It's a girl and it will STAY a girl. you're only flipping one coin. The odds of it being a boy is just as equal of it being a girl. 50 fucking 50.
 2nd April 2003, 21:22 #357 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 if you flip two coins X number of times, the change you get all heads is 1/4, you get all tails 1/4, and the change that you get a mix is 1/2. I still stand by my 2 answers though,
2nd April 2003, 21:57   #358
xzxzzx
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Quote:
 Originally posted by dlinkwit27 if you flip two coins X number of times, the change you get all heads is 1/4, you get all tails 1/4, and the change that you get a mix is 1/2. I still stand by my 2 answers though,
Exactly. And that is the point. I don't understand how you can "stand by" two opposing answers, though.

SSJ4_Gogitta, this is exactly what I'm talking about. You have not "flipped one coin" - because you don't know which coin I'm talking about.

Let's say you have a hat. You've got the following written on 4 pieces of paper:

GG GB BG BB

You pull out one of them, have someone else look at it, and ask them "is one of the letters 'G'?" - they answer "yes". You do it again, until all 4 have been pulled out of the hat. You will find that of the 3 times that there was a 'G', the other letter was 'B'. Or is it that you don't think {GG, GB, BG, BB} is the correct distribution of Gs and Bs?

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 2nd April 2003, 22:23 #359 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 The answer is 50/50 IT WILL EITHER BE A BOY OR A GIRL. No inbetween. It eiter will, or it wont. Equal chances. And it dosent matter wich coin you filp, each coin has a 50/50 chance of being heads. And you DID flip one coin. The other one has already been flipped, and was tales. It is the other coin we are worried about. We KNOW for a 100% FACT that the first child is a girl. The odds of the 2nd child, the 2nd coin, of being heads is 50/50. It either will, or it wont. ockham's razor states that the simplest answer tends to be the correct one. ITS LOGIC. It either will, or it wont be a boy. And again with the GG GB BG BB thing. ITS BULLSHIT. the GB BG are THE SAME. one boy, one girl. it DOES NOT MATTER if the girl is on the left, or the right. it states the SAME THING. you have a boy and a girl. Whats left is GG BB. 50/50 chance of picking either.
 2nd April 2003, 22:30 #360 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,160 How about this. We eliminate the girl. the girl never existed. We elimited a 100% chance of having a girl, so lets elimiate a 100% chance of having a boy. so GG BG GB BB narrows down to BG GB Now, waht are the odds of haivng a boy? 50/50. Now, say the first one IS a girl. Since there was a 50% chance of having a girl, there was a 50% chance of having a boy, there is no 100% chance of a boy. GG BG GB BB now narrows down to G BG GB B which is the same as GB GG BB since there are no 100% chances, it further reduces to: GB Now, it dosnet matter which one you pick, you still have a 50% chance of picking a boy.
 Winamp & SHOUTcast Forums Mathematical Logic [part 2]