Exercise 1.5
1. Using the adjacent Venn diagram, find
the following sets:
(i) A − B (ii) B -C (iii) A′ ∪ B′ (iv) A′ ∩ B′ (v) (B ∪C)′ (vi) A − (B ∪C) (vii) A − (B ∩C)
2. If K = { a , b, d, e, f } , L = { b,
c, d, g } and M = { a , b, c, d, h
} , then find the following:
(i) K ∪ (L ∩ M) (ii) K ∩ (L ∪ M) (iii) (K ∪ L ) ∩ (K ∪ M) (iv) (K∩ L) ∪ (K ∩ M)
and verify distributive laws.
3. If A = {x : x ∈ ℤ, −
2 < x ≤ 4}, B={x : x ∈ W , x ≤
5}, C = {−4, −1, 0, 2, 3, 4}, then verify
A ∪ (B
∩C ) = (A ∪ B )
∩ (A ∪C) .
4. Verify A ∪ (B ∩C ) = (A ∪ B ) ∩ (A ∪C) using Venn diagrams.
5. If A = {b, c,
e, g, h} , B = {a , c, d , g,
i } and C = {a , d, e, g, h} ,
then show that A−(B ∩C)
= (A−B)∪(A−C).
6. If A = {x : x
= 6n, n∈W and n<6}, B = {x
: x = 2n, n ∈ ℕ and 2<n≤9} and C = {x
: x = 3n, n ∈ ℕ and 4≤n<10},
then show that A − (B ∩
C ) = (A −
B ) ∪
(A −C)
7. If A = {–2,0,1,3,5}, B
= {–1,0,2,5,6} and C = {–1,2,5,6,7}, then show that A − (B
∪C) =
(A−B)∩(A−C).
8. If A = {y : y = [a + 1] /2 , a∈W and a ≤ 5}, B = {y : y = [2n -1] / 2, n∈W and n < 5} and C = {-1, -1/2,1,3/2,2},
then show that A − (B ∪ C )
= (A − B ) ∩ (A −C) .
9. Verify A − (B
∩ C
) = (A − B
) ∪ (A
−C) using
Venn diagrams.
10. If U = {4,7,8,10,11,12,15,16},
A={7,8,11,12} and B = {4,8,12,15} then verify De Morgan’s Laws for
complementation.
11. Verify (A ∩ B)′ = A′ ∪ B′ using Venn diagrams.
Related Topics
Privacy Policy, Terms and Conditions, DMCA Policy and Compliant
Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.