The Staircase of Falsity

Here's another math trick that's about logic instead of numbers! Can you guess how this math trick got its name?

P	Q	~P	~Q	P→~Q	P→Q	~P→~Q	~P→Q	P←~Q	P←Q	~P←~Q	~P←Q
TRUE	TRUE	FALSE	FALSE	FALSE	TRUE	TRUE	TRUE	TRUE	TRUE	TRUE	FALSE
TRUE	FALSE	FALSE	TRUE	TRUE	FALSE	TRUE	TRUE	TRUE	TRUE	FALSE	TRUE
FALSE	TRUE	TRUE	FALSE	TRUE	TRUE	FALSE	TRUE	TRUE	FALSE	TRUE	TRUE
FALSE	FALSE	TRUE	TRUE	TRUE	TRUE	TRUE	FALSE	FALSE	TRUE	TRUE	TRUE

Look at the truth values of the orange columns. Now look at the truth values of the blue columns. They form a staircase of falsity as you move to the next column! The orange columns go downward & the blue ones go upward!

The arrow performs the conditional function in truth tables & always points to the conclusion.

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

Some of the compound statements in the truth table above are logically equivalent! Can you guess which ones? I'll give you 1 example: (~P→~Q) = (P←Q)!

Note: "If P then Q" = "Not P or Q"

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