Logical Implication

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.


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.


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.


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”.

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