Question no. 4

samp X ContX Logic x C+x Progx Repl. x Repl. x Your x C++ X Contx 106 x Get+ x Que l earn-us-east-1-prod-fleet01-xythos.s3.us-east-1.amazonaws.com/5cc71db6522fe/10899529?response-content-dispositioninline%3B%20filename%2A%3DUTF-8 C nos x a b. There is no professor who has been asked a question by every student. C. There is a professor who has never been asked a question by any student. d. There is a student who has asked a question to exactly one professor. e. There are two different students who have asked each other a question. Part II: Proving logical equivalence using laws of propositional logic (50 pt.) 4. (35 pt.) Use the laws of propositional logic to prove that the following compound propositions are logically equivalent. a. (5 pt.) (p = q) v (p + r) and p (qur) b. (10 pt.) p = q and (p19) (-P4-9) C. (10 pt.) p + (p^q) and p q d. (10 pt.) -(p V (q^(rp))) and p^q r)