Biconditional Statement

$A⟺B$. This is equivalent to saying $A⟹B\cap B⟹A$. In other words, both statements must prove eachother. They are necessary and sufficient conditions for each other. If both statements are true.

Bi-conditional Anatomy

$P⟺Q$ $P\Leftarrow Q$ (if) $P⟹Q$ (only if)

Equivalent Logical Statement

$P⟺Q\equiv (P\wedge Q)\vee (\neg A\wedge \neg B)$ $P⟺Q\equiv (P\wedge Q)\vee (\neg A\wedge \neg B)$

Bi-conditional Negation

For the statement: $P\leftrightarrow Q$, the logical negation is: $(P\to \neg Q)\vee (\neg A\Rightarrow Q)$