[12 Points] In this problem, A(z) and B(x) are two predicates over the same domain. For example, the domain could be the set of Northeastern students, A(x) could mean "T passed course A and B(x) could mean "x passed course B. For each of the statements below, state whether it is true or false. If true, explain why each of its directions and is true. If false state which direction is false and give a counterexample. (a) Vr(A(z) V B(x)) + (VxA(1) V VB(x)) (b) Vx(A(2) AB(2) H (V2A(2) AVXB(x)) (c) Ex(A(2) V B(2)) 4 (3xA(2) V=xB(x)) (d) 3.0 (A2) AB(2) H (3. A3.c (2)