uppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either provide a proof to show that this is true or provide a counterexample to sh

6. The following statements about sets are false. For each statement, give an example, i.e., a choice of sets, for which the statement is false. Such examples are called counterexamples. They are examples that are counter to, i.e., contrary to, the assertion. (a) AUBCAn B for all A, B. (b) ANØ: = A for all A. (c) AN (BUC) = (A ^ B) UC for all A, B, C.

Prove that if A, B, and C are arbitrary sets and A −C ⊈ A −B, then B ⊈ C. I dont know how to prove this. I want to  contrapostive B⊆C, then A-C ⊆ A-B.

6. Use a direct proof technique to prove the following theorems: The sets A, B, and C are arbitrary subsets of some universal set U. Prove that (C – A) U (C – B) = C – (An B).