Conditional Statement

$P⟹Q$.

If $P$ is true, than $Q$ is true. $P$ is the condition/antecedent and $Q$ is the result/consequent Can also be $Q\Leftarrow P$,

Examples

$x$ is odd $\cap$ $y$ is odd $⟹$ $x+y$ is even This is not true backwards where $x+y$ is even $⟹$ $x$ is odd $\cap$ $y$ is odd an easy Proof By Counter Example for this is x = 2 and y = 4

Proof Writing

$P⟹Q$ First assume p is true, then show Q is also true.

Contrapositive Law

$P⟹Q\equiv \neg Q⟹\neg P$

Negated Conditional Statements

$\neg (P⟹Q)\equiv P\wedge \neg Q$

English Sayings

1. P implies Q
2. Q, if P
3. P only if Q
4. P is a sufficient condition for Q
5. Q is a necessary condition for P

Concepts

• Vacuously True
• Conditional Statement Truth Table