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 
Some compound statements of the 1st truth table are logically equivalent!
Back to Index Page Back to Math Trick Menu
© Derek Cumberbatch