3 Part III 1. Let A and B be sets. Show that a. (A ∩ B) ⊆ A b. A ⊆ (A ∪ B) c. A − B ⊆ A d. A ∩ (B − A) = ∅ e. A ∪ (B − A) = A ∪ B

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(1)(a) We have to prove (A nn B)sube ALet x in A nn B, by definition of intersection x in A. and x in B. Thus in particuler, x in A is trueHence x in A nn B=>x in A=>quad A nn B sube A(b) we have to prove A sube A uu BLet x in A, Thus, it is true that at least one of x in A or x in B is true. since x in A or x in B true, by definition of union x in A uu BHence x in A=>x in A uu B=>A sube A uu B(c) A-B sube-ALet x in A-B, By definition of set differen ... See the full answer