Logical Implication

The implication of Q by P is the proposition (¬P) ∨ Q, noted as “P ⇒ Q” or “P implies Q” which is false only if the proposition P is true and the proposition Q is false. The implication is true in all other cases.

Symbol

The symbol of a logical implication is “P ⇒ Q” which is read as “P implies Q”.

In other words, P ⇒ Q means that the conditional P → Q is always true.

Property

The truth table of a logical implication is:

P	Q	P ⇒ Q
1	1	1
1	0	0
0	1	1
0	0	1

In which 1 = true and 0 = false.

Example

Consider the propositions “P: the quadrilateral ABCD is a square” and “Q: the quadrilateral ABCD is a rectangle“.
Therefore, we have the logical implication “P ⇒ Q” which is read like this: “if the quadrilateral ABCD is a square, then the quadrilateral ABCD is a rectangle”.