Let * be a binary logical connective that makes (P*Q)^(Q*P) logically equivalent to PQ. Show that.....

if in addition P * Q is not always true, then * is 2.37 Remark. Let * be a binary logical connective. In Theorem 2.17, we saw that (P Q)A(Q > P) is logically equivalent to PQ. Similarly, it is easy to see that (PQ) / (Q P) is logically equivalent to P Q. Finally, it should be obvious that (P Q) (QP) is logically equivalent to P Q. Thus ly equivalent to P# Q. In part (a) if * is or if * is +., or if * is , then (P * Q) ^ (Q * P) is logical of the next exercise, you are asked to prove the converse of this. Exercise 34. Let * be a binary logical connective that makes (L, Q)A (Q * P logically equivalent to (a) Show that * is , or * is , or * is. In other words, show that the truth table for * is the same as the truth table for or the truth table for ., or the truth table for f. (Warning: In my experience, many students do not solve this exercise correctly. Instead, they prove the converse of what is asked. In other words, they just reprove the facts that are pointed out in Remark 2.37 Then figure out as much as you can about T F and F * T.) (b) Now suppose in addition that * makes (RAS) *R a tautology. Show that then * is . In other words, show that the truth table for * is the same as the truth table for . (The warning for part (a) applies here too. Hint: Combine part (a) of this exercise with Example 2.35(a))