Problem 4 125pts] a) [9pts] For each of the following set of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion(s) from the premises a. [3pts] "IfI play hockey, then I am sore the next day." "I use the whirlpool if I am b. [3pts| "I am dreaming or hallucinating." "I am not dreaming." "If I am c. [3pts] "If I take the day off, it either rains or snows." "I took Tuesday off or I took sore. I did not use the whirlpool." hallucinating, I see elephants running down the road." Thursday off." "It was sunny on Tuesday." "It did not snow on Thursday." [Assume that if it is sunny, then it is neither raining nor snowing] b) [16pts] Show that if n is an integer and 3n+ 2 is even, then n is even using the followinjg proof techniques. Show all your work, [8pts] Proof by contraposition [8pts] Proof by contradiction