Single Simple Statements Can Create Tautologies!

This math trick is about logic. A single simple statement can be used to create tautologies! (Or contradictions if you use the "NOT" function) The 1st truth table below uses biconditionals & exclusive disjunctions.

P	~P	P = P	~(P = P)	P ≠ P	~(P ≠ P)	(P = P) = ~(P ≠ P)	~(P = P) = (P ≠ P)
TRUE	FALSE	TRUE	FALSE	FALSE	TRUE	TRUE	TRUE
FALSE	TRUE	TRUE	FALSE	FALSE	TRUE	TRUE	TRUE

The tilde (~) represents the negation function in logic. When you use the word not in a sentence, you are using the negation function. It flips the truth value of a statement.

Using 1 simple statement also makes tautologies with the conditional(If...then...) function! But not with conjunctions or inclusive disjunctions. The "neither...nor..." function can't make tautologies or contradictions with 1 simple statement, either.

P	~P	P & P	P or P	P→P	P nor P
TRUE	FALSE	TRUE	TRUE	TRUE	FALSE
FALSE	TRUE	FALSE	FALSE	TRUE	TRUE

The letter P represents any simple statement in the truth table above.

Some compound statements of the 1st truth table are logically equivalent!

Back to Index Page Back to Math Trick Menu