(1) Using the adjacent Venn diagram, find the following sets:
(i) A - B (ii) B - C (iii) A' U B' (iv) A' n B' (v) (B U C)'
(vi) A − (B U C) (vii) A − (B n C) Solution
(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 U (L n M) (ii) K n (L U M) (iii) (K U L) n (K U M)
(iv) (K n L) U (K n 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 U (B n C) = (A U B) n (A U C). Solution
(4) Verify A U (B n C) = (A U B) n (A U C) using Venn diagrams Solution
(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 n C) = (A − B) U (A−C) . Solution
(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 n C) = (A − B) U (A − C) Solution
(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 U C) = (A − B) n (A − C) Solution
(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 - (BUC) = (A - B) n (A - C) Solution
(9) Verify A − (B n C) = (A − B) U (A − C) using Venn diagrams. Solution
(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. Solution
(11) Verify (A n B)' = A' U B' using Venn diagrams. Solution
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