4. (18 points) Suppose that we are trying to describe Fred Luddy's sock drawer using first-order logic. We let our universe be all of the socks in Luddy's drawer, and define the following predicates: 1. L(2): is lime. 2. M(x): 1 is maroon. 3. P(, y): r is paired with y. 4. C: Luddy is cool. Given the premises VrVyPr,y) P(y, 2) VzVyz (P(x,y) Ay #2) c- (vz L() (By : M (1) A P(x,v)) C- (M() =(au: Lt)P(x,y))) (L(z) M(x)) (-Z(z) ^M(-))) (31,5 (M(z)^M) A P(z.)) (L(*) ^ Z(w) P(x, y))) --- C + | Vr use resolution to prove that 4. (18 points) Suppose that we are trying to describe Fred Luddy's sock drawer using first-order logic. We let our universe be all of the socks in Luddy's drawer, and define the following predicates: 1. L(2): is lime. 2. M(x): 1 is maroon. 3. P(, y): r is paired with y. 4. C: Luddy is cool. Given the premises VrVyPr,y) P(y, 2) VzVyz (P(x,y) Ay #2) c- (vz L() (By : M (1) A P(x,v)) C- (M() =(au: Lt)P(x,y))) (L(z) M(x)) (-Z(z) ^M(-))) (31,5 (M(z)^M) A P(z.)) (L(*) ^ Z(w) P(x, y))) --- C + | Vr use resolution to prove that