# 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

 Jun 22, 2011 Logic - Truth Table by: Staff The question: by Claudia (San Antonio TX)use a truth table to prove: (~pvq)^pv q=qThe 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 tautologyThanks for writing.Staff www.solving-math-problems.com