10. (1.3 Propositional Equivalence) Which of the following is a tautology? a. [(p = q) r] + [p (q + r)] b. [(p19) r] + [(p +r)^(q r)] C. (poq) + (p = q) d. (p = q) + (-9 up) 11. (1.6 Rules of Inference) What relevant conclusion or conclusions and what rules of inference are used to obtain each conclusion from the following premises. If I play hockey, then I am sore the next day." "I use the whirlpool if I am sore." "I did not use the whirlpool. a. Modus Tollens, I am sore, and I play hockey. b. Modus Tollens, I am not sore, and I did not play hockey. C. Modus Ponens, I use the whirlpool, and I am not sore the next day. d. Simplification, I play hockey and I use the whirlpool. 4 Discrete Structures CMSC 2123 CRN 11094 IVE CRN 15441 Test 1 Version 1 Autumn 2020 12. (1.6 Rules of Inference) Supply the missing statement in the following argument: Statement Reason 1 (p1q) -r1-5) Premise 2 77(01) Premise 3 1, 2, Modus Tollens a. (r AS) b. p va C. (pvq) d. -(p19)