My Math Forum Truth Table problem

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 October 28th, 2011, 10:00 AM #1 Newbie   Joined: Oct 2011 Posts: 3 Thanks: 0 Truth Table problem Hello, I'm currently working on a truth table, and I seem to have a problem with grasping some of the concepts. I'm trying to figure this out: (p -> q) <-> (-q -> -p). If you're used to different symbols, this is the text version: (p if then q) if and only if (not q if then not p) p q p -> q -q => -p (p -> q) <-> (-q -> -p) 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 Am I right, or way off? -Akhanoth
 October 28th, 2011, 10:12 AM #2 Newbie   Joined: Oct 2011 Posts: 3 Thanks: 0 Re: Truth Table problem p q.........p -> q.......-q => -p.........(p -> q) <-> (-q -> -p) 0 0.........1.................1..................... ....1 0 1.........1.................1..................... ....0 1 0.........0.................0..................... ....0 1 1.........1.................1..................... ....1 had to do it like this, couldn't get the multiple spaces to work =p
 October 28th, 2011, 11:29 AM #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: Truth Table problem Your method is right, and your first two (or four if you count the variables) columns are right. But the last column is p <-> q when it should be (p -> q) <-> (-q -> -p). Just put a 1 when the two columns immediately to the left are the same and a 0 when they are different.
 October 28th, 2011, 11:44 AM #4 Newbie   Joined: Oct 2011 Posts: 3 Thanks: 0 Re: Truth Table problem Thanks a lot for the help! Does that go for every situation? Or simply because it's a <-> in between?
October 28th, 2011, 06:10 PM   #5
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Re: Truth Table problem

Hello, Akhanoth!

Quote:
 $\text{Construct the truth table for: }\:(p\,\to\,q)\:\leftrightarrow\:(\sim q\,\to\,\sim p)$

[color=beige]. . [/color]$\begin{array}{|c|c|c|c|ccc|}p & q & p\,\to\,q & \sim q\,\to\,\sim p & (p\,\to\,q) & \leftrightarrow & (\sim q\,\to\,\sim p) \\ \\ \hline \\ \\ T & T & T & T && T& \\ \\ T & F & F & F && T & \\ \\ F & T & T & T && T & \\ \\ F & F & T & T && T & \\ \\ \hline \end{array}$

October 29th, 2011, 07:38 AM   #6
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Re: Truth Table problem

Quote:
 Originally Posted by Akhanoth Thanks a lot for the help! Does that go for every situation? Or simply because it's a <-> in between?
In every situation you can reduce a big problem to smaller problems and fill out the truth table by combining two existing columns with some standard operation. In this case the operation was <-> "are the two columns the same". Was the operation something else you'd do something else.

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