August 7th, 2012, 05:39 PM  #1 
Newbie Joined: Aug 2012 Posts: 5 Thanks: 0  Symbolic logic
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August 7th, 2012, 05:49 PM  #2 
Newbie Joined: Aug 2012 Posts: 5 Thanks: 0  Re: Symbolic logic
Sorry, newbie here So I am to translate the following argument in symbolic logic: If John gets the teaching position and works hard, then his salary will double. If his salary doubles, then he will offer a party to his friends. He has not offered a party to his friends. Therefore, either he did not get the teaching position or he did not work hard. I'm just a little confused as to how to put it all together. Let A = gets teaching position B = works hard C = salary doubles D = party I have the components (A^B) > C C>D Can this be put together as [(A^B)>C]>D ? Now the second part is: (* being used as "not" because I can't find that symbol, also can't find the symbol for "or") *D > (*Aor*B) How is that connected to the first part? Or are they stated as two separate statements? Thanks for your help! 
August 7th, 2012, 06:08 PM  #3  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Symbolic logic Quote:
Quote:
What you can conclude is that (A^B) > D since C implies D. Quote:
is the same as not(not(D)) or (not(A) or not(B)) which is D or not(A) or not(B) which is not(A) or not(B) or D which can be written using DeMorgan's law as not(A^B) or D which is the same as (A^B)>D.  
August 7th, 2012, 07:15 PM  #4 
Newbie Joined: Aug 2012 Posts: 5 Thanks: 0  Re: Symbolic logic
Thank you so much!

August 8th, 2012, 04:57 AM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Symbolic logic Hello, jojoluvsu2! Quote:
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