“A implies B”, written symbolically as $A⟹B$, is defined by the truth table:

\hline
A & B & A \implies B\\
\hline
T & T & T\\
T & F & F\\ F & T & T\\ F & F & T\\
\hline
\end{array}

$A$ is referred to as the **hypothesis** for the implication, and $B$ is referred as the **conclusion**.

#### The Inverse

The implication $(¬A)⟹(¬B)$ is the **inverse** of $A⟹B$

#### The Converse

The implication $B⟹A$ is the **converse** of $A⟹B$

#### The Contrapositive

The implication $(¬B)⟹(¬A)$ is the **contrapositive** of $A⟹B$
$(A⟹B)≡((¬B)⟹(¬A))(logically equivalent)$

##### Other remarks

$((A∨B)⟹C)≡((A⟹C)∧(B⟹C))$ $(A⟹B)≡((¬A)∨B)$ $¬(A⟹B)≡(A∧(¬B))(negation of implication)$