Suppose that p is a statement that is logically true. What is its truth set? Now p is logically true if and only if it is true in every logically possible case, so that the truth set of p must be U. Similarly, if p is logically false, then it is false for every logically possible case, so that its truth set is the empty set ∅. Finally, let us consider the implication relation. Recall that p im- plies p if and only if the conditional p → q is logically true. But p → q is logically true if and only if its truth set is.
