# Every Logical Expression is either a Tautology or Contradiction

The question ask if the above claim is True or False. if true I Must prove that and give a counter example if it is false.

I prefer the claim to be false.

since looking at every logical expression either a conditional P then Q statement or bi-conditional statement the last column will always be T=TRUE. therefor I conclude it is false since the last column of every logical expression will always be true.

I'm I correct or there is a law or example to prove it is true.

• Consider the expression $p$ for any propositional variable $p$. It's neither a tautology, nor a contradiction. – Stefan Mesken Mar 31 '16 at 23:09
• I am confused about your explanation above, would you be able to clarify? – Inazuma Mar 31 '16 at 23:21
• I agree (it's true) that the claim is false (as @Stefan notes, consider the formula $p$); but I don't understand the reasons you give. In fact, I don't understand your second to last paragraph at all. – BrianO Mar 31 '16 at 23:22
• I am referring to the last column of the truth table . in which is true for every expression. – Surdz Mar 31 '16 at 23:27
• The truth table values p -> q (conditional) or a p <-> q (biconditional) is not all true, and if it was, that would make it a tautology. – Inazuma Mar 31 '16 at 23:31