Logic Notions

Implication: p ⇒ q

The implication p ⇒ q ('p implies q', or else 'if p then q') is the proposition which is FALSE if p is TRUE and q is FALSE, and TRUE otherwise.

  p  |  q  |  p⇒q

  T  |  T  |   T

  T  |  F  |   F

  F  |  T  |   T

  F  |  F  |   T

Remark: when we consider p ⇒ q, p is referred to as the HYPOTHESIS and q the THESIS.

Bi-implication: p ⟺ q 

The bi-implication p ⟺ q ('p is equivalent to q', or else 'p if and only if q') is the proposition which is TRUE if p, q have the same logic value, and FALSE otherwise.

  p  |  q  |  p⟺q

  T  |  T  |   T

  T  |  F  |   F

  F  |  T  |   F

  F  |  F  |   T