5-(6 points) Anume the domain centains eveny thirg. Using the given predicates, write lagiral expressions for the following sentences: D(x):x is a day S(x):x is sumny R(x):x is rainy M: Monday T: Tuestay (a) Some days are sunny and rainy. (b) Both Mowlay and Twesdby are rainy (c) Every day that is rainy is not sumny. 6- 17 points) Using logical equivalences ad rules of inference. prove that if x(P(x)Q(x)) then xP(x)xQ(x). 7 - ( 12 points) Using logical equivalences and rules of inderence prove that if x(L(x)R(x)) and Jx(P(x)R(x)) then x(P(x)L(x)). 8- (9 points) Given the hypotheres x(A(x)B(x)) and x(A(x)P(x)) prove the conclusion x(P(x)B(x))