My Math Forum truth table, how to build a truth table with these informations

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 February 4th, 2017, 06:46 AM #1 Newbie   Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 truth table, how to build a truth table with these informations I would like to know how to build a truth table with these information Please? If Mike hits the wall on the east OR on the west, then Mike goes backwards 30 steps, then Mike turn to a random direction AND goes forward again.
 February 4th, 2017, 06:50 AM #2 Senior Member   Joined: Dec 2012 From: Hong Kong Posts: 781 Thanks: 284 Math Focus: Linear algebra, linear statistical models Let's use these symbols: P: Mike hits the wall on the east Q: Mike hits the wall on the west R: Mike goes backward 30 steps S: Mike turns to a random direction T: Mike goes forward again The first part we can formalise as (P V Q), since 'or' appeared. The second part we can write as (R & S & T) - don't be deceived by the 'then', which indicates time rather than conditionality. We put the whole thing together like this: (P V Q) -> (R & (S & T)). The truth table should be routine. Can you continue? Thanks from Gab Last edited by 123qwerty; February 4th, 2017 at 07:05 AM.
 February 4th, 2017, 06:56 AM #3 Newbie   Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 Thanks very much already, actually I would like to get the truth table if you don't mind please, Can you continue? thanks again.
 February 4th, 2017, 07:08 AM #4 Senior Member   Joined: Dec 2012 From: Hong Kong Posts: 781 Thanks: 284 Math Focus: Linear algebra, linear statistical models Hmm, it's a tad hard to represent tables in the forum (I've tried \begin{tabular} in LaTeX and it didn't work). I can provide you with a few representative examples so that you can work out the rest yourself. Code: P | Q | R | S | T | (P v Q) -> (R & (S & T)) T | T | T | T | T | T T T T T T T T T T | F | T | T | F | T T F F T F T F F F | F | T | T | T | F F F T T T T T T F | F | T | T | F | F F F T T F T F F Thanks from Gab Last edited by 123qwerty; February 4th, 2017 at 08:07 AM.
 February 4th, 2017, 12:16 PM #5 Newbie   Joined: Jan 2017 From: ireland Posts: 8 Thanks: 0 Hello. I would like to reduce the same compound proposition to a Conjunctive Normal Form, Do you know, thank. (P V Q) -> (R & (S & T)).

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