The negation of :pis the statement with the opposite truth value as :p, thus :(:p) is just another name for p. The negation of p^qasserts \it is not the case that pand qare both true". Thus, :(p^q) is true exactly when one or both of pand qis false, that is, when :p_:qis true. Similarly, :(p_q) can be seen to the same as :p^:q.

Properties of matter lab middle schoolConverse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause.

Implication: "p -> q" or "p implies q" means that whenever p is TRUE, so is q. The only way "p -> q" can be FALSE, is if p is TRUE, and q is FALSE. Equivalence: "p == q" means that p and q have the same value. NAND: "p NAND q" is the same as "NOT (p AND q)". NOR: "p NOR q" is the same as "NOT (p OR q)".