# Prove that #(not(p rarr q) ^^ (p harr notq)) harr ((p ^^ notq)) #?

##### 1 Answer

Feb 20, 2017

We can build a truth table for each of the statements.

Since the truth values for:

#not(p rarr q) ^^ (p harr notq)# and#(p ^^ notq)#

are exactly the same for all possible combinations of truth values of

#(not(p rarr q) ^^ (p harr notq)) harr ((p ^^ notq)) #

is a tautology and therefore the two propositions are equivalent. QED