Logical Operations and Truth Tables
A mathematical sentence is a sentence that states a fact or contains a complete idea. A sentence that can be judged to be true or false is called a statement.
The statement can be true (T) or false (⊥).
P, Q, R,... statements
Example:
This girl is beatiful.  not a statement.
Today is Wensday.  statement.
Negation ($\neg $) (not)
$P$

$\neg P$

$$\top $$

$$\perp $$

$$\perp $$

$$\top $$

Disjunction ($\vee $) (or)
$P$

$Q$

$P\vee Q$

$$\top $$

$$\top $$

$$\top $$

$$\top $$

$$\perp $$

$$\top $$

$$\perp $$

$$\top $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

Conjunction ($\wedge $) (and)
$P$

$Q$

$P\wedge Q$

$$\top $$

$$\top $$

$$\top $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

$$\perp $$

Implication ($\Rightarrow $) (if ... than...)
$P$

$Q$

$P\Rightarrow Q$

$$\top $$

$$\top $$

$$\top $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

$$\top $$

$$\top $$

$$\perp $$

$$\perp $$

$$\top $$

Equality ($\iff $) (if and only if)
$P$

$Q$

$P\iff Q$

$$\top $$

$$\top $$

$$\top $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

$$\top $$

$$\perp $$

$$\perp $$

$$\perp $$

$$\top $$

Keywords: logic, true, false, negation, disjunction, conjunction, implication, equality