stylistic:tone, structural:summarization, structural:expansion
Logical implication

Logical implication and the material conditional are both associated with an operation on two logical values, typically the values of two propositions, which produces a value of false if the first operand is true and the second operand is false, and a value of true otherwise.

The truth table associated with the logical implication p implies q (symbolized as p ⇒ q, or more rarely Cpq) is as follows:

The truth table associated with the material conditional if p then q (symbolized as p → q) is as follows:

p ⇒ q and p → q are equivalent to ¬p ∨ q.