The implication q ⇒ p is read as ‘if q, then p’. When this is true, q is a sufficient condition for p; that is, the truth of the ‘condition’ q is sufficient to ensure the truth of p, or equally that ‘p is true if q is true’. It is also said that p is a necessary condition for q; the truth of p is a necessary consequence of the truth of q, or equally ‘q is true only if p is true’. When the implication between p and q holds both ways, p is true if and only if q is true, which may be written p⇔q. Then q is a necessary and sufficient condition for p.