Q3 of 145 Page 36

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).


(i) Given:


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


BC = {e, o} and A(BC) = {a, e, I, o, u}


B


C


RHS:


AB = {a, d, e, I, o, u, v} and AC = {a, e, I, o, u, t, m}



(A B) (A C) = {a, e, I, o, u}


LHS = RHS. [Verified].


(ii) Given:


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


BC = {a, d, v, e, o, t, m} and A(BC) = {a, e, o}


B


C


RHS:


AB = {a, e, o} and AC = {e, o}



(A ∩ B) ∪ (A ∩ C) = {a, e, o}


LHS = RHS. [Verified]


More from this chapter

All 145 →
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)


 2

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).


 4

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

 5

Let A = {2, 3, 5, 7, 11, 13}, B = {5, 7, 9, 11, 15} be subsets of U = {2, 3, 5, 7, 9, 11, 13, 15}.

Using Venn diagrams, verify that:


(i) (A ∪ B’) = (A’ ∩ B’)


(ii) (A ∩ B)’ = (A’ ∪ B’)