Posted by angela on Friday, June 1, 2012 at 10:07pm.
Given p is false, q is true,and r is false, find the truth value of the statement. (~P <____> ~Q) ____> ~r
Show step by step work.

geometry  MathMate, Friday, June 1, 2012 at 11:08pm
The <> operator is true only if both operands have the same truth value, i.e. TT or FF.
Given p is false and q is true, then ~p is true and ~q is false, therefore ~p <> ~q is false.
Since the conditional p>q is false only if p is true and q is false, here we have
F>~r or
F>T
so it is true. Thus with p=F, q=T and r=F, the whole statement together is true,