Q2 of 145 Page 36

Let A = {2, 4, 6, 8, 10}, B = {4, 8, 12, 16} and C = {6, 12, 18, 24}.

Using Venn diagrams, verify that:


(i) (A ∪ B) ∪ C = A ∪ (B ∪ C)


(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C).


(i) LHS:


AB = {2, 4, 6, 8, 10, 12, 16} (AB)C = {2, 4, 6, 8, 10, 12, 16, 18, 24}


A


B


RHS:


BC = {4, 6, 8, 10, 12, 16, 18, 24}


BC


A(BC) = {2, 4, 6, 8, 10, 12, 16, 18, 24}



LHS = RHS. [Verified]


(ii)LHS:


AB = {4, 8} (AB)C = {} or ø


A


B


RHS:


BC = {12} A(BC) = {}



LHS = RHS.[Verified]


More from this chapter

All 145 →
8

For any sets A and B, prove that:

(i) A ∩ B’ = ϕ ⇒ A B


(ii) A’ ∪ B’ = U ⇒ A B


 1

Let A = {a, b, c, e, f} B = {c, d, e, g} and C = {b, c, f, g} be subsets of the set U = {a, b, c, d, e, f, g, h}.

(i) A ∩ B


(ii) A ∪ (B ∩ C)


(iii) A – B


(iv) B – A


(v) A – (B ∩ C)


(vi) (B – C) ∪ (C – B)


 3

Let A = {a, e, I, o, u}, B = {a, d, e, o, v} and C = {e, o, t, m}.

Using Venn diagrams, verify the following


(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)


(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).


 4

Let A ⊂ B ⊂ U. Exhibit it in a Venn diagram.