Logical equivalence - SS2 Mathematics Lesson Note

A situation of logical equivalence arises when the truth values of two compound statements are the same. For instance, an implicative statement and a contradiction are logical equivalents. So is a converse and inverse statement.

	Implication	Converse	Inverse	Contrapositive
\[\mathbf{p}\]	\[\mathbf{q}\]	\[\mathbf{\sim p}\]	\[\mathbf{\sim q}\]	\[\mathbf{p \Rightarrow q}\]	\[\mathbf{q}\mathbf{\Rightarrow}\mathbf{p}\]	\[\mathbf{\sim p}\mathbf{\Rightarrow}\mathbf{\sim q}\]	\[\mathbf{\sim q}\mathbf{\Rightarrow \sim p}\]
\[T\]	\[T\]	\[F\]	\[F\]	\[T\]	\[T\]	\[T\]	\[T\]
\[T\]	\[F\]	\[F\]	\[T\]	\[F\]	\[T\]	\[T\]	\[F\]
\[F\]	\[T\]	\[T\]	\[F\]	\[T\]	\[F\]	\[F\]	\[T\]
\[F\]	\[F\]	\[T\]	\[T\]	\[T\]	\[T\]	\[T\]	\[T\]