[4] Let A andB be sets such that A C B. Prove that A OBC B, using an argument that starts with "Take any x E AOB ...". Then use the universe U = {1,2} to demonstrate that A BĘ B is possible.

Q: 19. For all sets A, B, and C, if AC BandACC then AC BnC.

A:

Q: Consider an indexed family of sets. B={Bn:neN}, where Bn = {2n, 2n + 1, 2n+2, ..., 3n}. (a) Write…

A:

Q: (b) Let={A i EN} be a family of sets with A₁ CA₂ CCA10 C... Prove that nA = A₁.

A:

Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

Q: Exercise 3.3.15. Prove or find a counterexample to the following statement. Let A, B and C be sets.…

A: We have a statement  Let A, B and C be sets. Then (A - B) U C = (A U B U C) - (A ∩ B).

Q: Let A, B, C be sets. Prove A U (B and C) = (AUB) and (AUC)

A:

Q: c) [5 marks] Let A, B be any two sets. Prove that if A C B, then An B = 4.

A: * The intersection of complementary sets is empty.