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Logic - Truth Table

by Claudia
(San Antonio TX)












































use a truth table to prove:

(~pvq)^pv q=q

∧: "and" symbol
∨: "or" symbol
~: "negation" (not) symbol

It is possible that this expression is a is a tautology (a logical statement where the conclusion is equivalent to the premise) .

Comments for Logic - Truth Table

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Jun 22, 2011
Logic - Truth Table
by: Staff


The question:

by Claudia
(San Antonio TX)


use a truth table to prove: (~pvq)^pv q=q


The answer:

∧: "and" symbol
∨: "or" symbol
~: "negation" (not) symbol


......p....q....~p

1....T....T.....F
2....T....F.....F
3....F....T.....T
4....F....F.....T


......q....~p....~p∨q

1....T......F..........T
2....F......F..........F
3....T......T..........T
4....F......T..........T


......p....~p∨q.....(~p∨q)∧p

1....T.........T................T
2....T.........F................F
3....F.........T................F
4....F.........T................F


......q....(~p∨q)∧p ....(~p∨q)∧p∨q

1....T.............T........................T
2....F.............F........................F
3....T.............F........................T
4....F.............F........................F


IMPORTANT Observation: the column for "q" and the column for (~p∨q)∧p∨q are exactly the same. This means that (~p∨q)∧p∨q →q is ALWAYS TRUE:


......q....(~p∨q)∧p∨q ....(~p∨q)∧p∨q →q

1....T..............T...........................T
2....F..............F...........................T
3....T..............T...........................T
4....F..............F...........................T


(~pvq)^pvq →q is a tautology





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Staff
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