11. (8pts) Translate the following into English, where R(x) is " x is a rabbit", H(x) is " x hops" and M(x) is " x knows math". The universe of discourse is all animals. (a) xH(x) (b) x(R(x)M(x)) (c) x((H(x)M(x))R(x)) (d) x(R(x)(H(x)M(x)))xR(x) 12. (8pts) Let Q(x,y,z) be the statement x2+y2=z2. If the domain consists of positive integers, what is the truth value of each item below? (a) Q(7,12,13)(Q(3,4,5) (b) xQ(x,1,x+1) (c) mn,Q(m2n2,2mn,m2+n2) (d) xyQ(x,y,x+y) 13. (8pts) Convert the following English statements into predicate logic expressions. Be sure to state your predi- cates, for example: "Let D(x) be the predicate ' x can dance".' The universe of discourse is all humans. (a) Not everyone loves to cook. (b) At least one person who does not love winter can skate. (c) Not all who wander are lost. (d) There is exactly one girl who can do miracles. 14. (6pts) Express the negation of the following statements in English. Do not use the word "not" in either of your solutions. Start by converting each sentence into a predicate logic expression. Then rework and simplify the expression until there are no negation symbols (). Then convert back to English. (a) There is someone who drives a car without an insurance. (b) There is at least one angel without wings. (c) All foxes do not have soft paws