The last column in the truth table of the statement pattern [p (q p)] [(p q) p] is

Step-by-step solution

We analyze the statement S = [p (q p)] [(p q) p] by constructing its truth table for all truth value combinations of p and q . Let p and q each take values true (T) and false (F). The subexpression q p is true only when q is true and p is false. Consequently, p (q p) is false when p is true and q p is false, which occurs for p true regardless of q ; otherwise, it is true. The expression p q is true unless both p and q are false, i.e., when p is false and q is true. Then (p q) p simplifies to p by absorption, since