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February 4th, 2017, 05:46 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, 05:50 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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? Last edited by 123qwerty; February 4th, 2017 at 06:05 AM. 
February 4th, 2017, 05:56 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, 06:08 AM  #4 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
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 Last edited by 123qwerty; February 4th, 2017 at 07:07 AM. 
February 4th, 2017, 11:16 AM  #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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