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 August 7th, 2012, 05:39 PM #1 Newbie   Joined: Aug 2012 Posts: 5 Thanks: 0 Symbolic logic S
 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
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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.

 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
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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.

$\text{Let: }\:\begin{Bmatrix}T=&\text{gets teaching job} \\ \\ \\ W=&\text{works hard} \\ \\ \\ D=&\text{salary doubles} \\ \\ \\ P=&\text{offers party} \end{Bmatrix}=$

$\text{The argument looks like this:}$

[color=beige]. . [/color]$\begin{array}{ccc}(T\,\wedge\,W) \;\to\; D \\ \\ \\ D \; \to\; P \\ \\ \\ \sim P \\ \\ \hline \\ \\ \sim T \:\vee\: \sim W \end{array}$

$\text{Another form:}$

[color=beige]. . [/color]$\bigg(\,\big[(T\,\wedge\,W) \:\to\;D\big]\:\wedge\:\big[D\:\to\:P\big] \:\wedge\: \big[\sim P\big]\,\bigg) \;\to\;(\sim T\,\vee\,\sim W)$

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