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August 7th, 2012, 04:39 PM   #1
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Symbolic logic

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August 7th, 2012, 04:49 PM   #2
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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!
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August 7th, 2012, 05:08 PM   #3
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Re: Symbolic logic

Quote:
Originally Posted by jojoluvsu2
I have the components

(A^B) --> C
C-->D
Right.

Quote:
Originally Posted by jojoluvsu2
Can this be put together as [(A^B)-->C]-->D ?
No. You know that (A^B)-->C, so your statement would be TRUE-->D or D and you do not know D. In fact, you know that D is false!

What you can conclude is that (A^B) --> D since C implies D.

Quote:
Originally Posted by jojoluvsu2
*D --> (*Aor*B)
not(D) --> (not(A) or not(B))
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.
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August 7th, 2012, 06:15 PM   #4
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Re: Symbolic logic

Thank you so much!
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August 8th, 2012, 03:57 AM   #5
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Re: Symbolic logic

Hello, jojoluvsu2!

Quote:
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.






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