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!
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© Derek Cumberbatch