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Table 2.21 Let p(x),q(x) be open statements defined for a given universe. The open statements p(x) and q(x) are called (logically) equivalent, and we write x[p(x)q(x)] when the biconditional p(a)q(a) is true for each replacement a from the universe (that is, p(a)q(a) for each a in the universe). If the implication p(a)q(a) is true for each a in the universe (that is, p(a)q(a) for each a in the universe), then we write x[p(x)q(x)] and say that p(x) logically implies q(x)