Implication & Negation With 1 Simple Statement

Here's another math trick that's about logic instead of numbers!

Depending on where the tilde (~) is in the 1st 2 implications, they're logically equivalent to either the simple statement, which is P, or its negation. (~P) The compound statements highlighted in gold are tautologies! (Tautologies are special compound statements that can't be used to tell a lie because they're always true, no matter what the case is!) With tildes next to both P's or not, the implication becomes a tautology!

Conditional statements are only false when the input behind the arrow is true but the input in front of the arrow is false.

In this 2nd truth table, the conditional arrows point to the left instead of the right:

The only 2 columns that "flipped" truth values are the 3rd & 4th ones since the arrow is pointing in the opposite direction from the 1st truth table.

Well, that's it already! There's no more left to explain about this math trick! However, Brain wants to remind you of something about logic:

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© Derek Cumberbatch