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February 4th, 2017, 06:46 AM   #1
Gab
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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.
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February 4th, 2017, 06:50 AM   #2
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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?
Thanks from Gab

Last edited by 123qwerty; February 4th, 2017 at 07:05 AM.
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February 4th, 2017, 06:56 AM   #3
Gab
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Thanks very much already, actually I would like to get the truth table if you don't mind please, Can you continue? thanks again.
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February 4th, 2017, 07:08 AM   #4
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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.
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February 4th, 2017, 12:16 PM   #5
Gab
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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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