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(Solved) : 12 Points Problem Z B X Two Predicates Domain Example Domain Could Set Northeastern Studen Q43918605 . . .

[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 VæB(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) Show transcribed image text [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 VæB(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)

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Answer to [12 Points] In this problem, A(z) and B(x) are two predicates over the same domain. For example, the domain could be the…