PRACTICE QUESTIONS WORKSHEET ON DEMORGAN LAW

(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.

Solution

(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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