Question 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 :
(i) A - B = {4, 6, 3}
(ii) B - C = {-1, 5, 7}
(iii) A' U B'
A' = {-3, 0, 1, 2, 5, 7, 8}
B' = {-3, 0, 1, 2, 3, 4, 6}
A' U B' = {-3, 0, 1, 2, 3, 4, 5, 6, 7, 8}
(iv) A' n B'
A' n B' = {-3, 0, 1, 2}
(v) (B U C)'
B U C = {-3, -,2, -1, 0, 3, 5, 7, 8}
(B U C)' = {4, 6, 1, 2}
(vi) A − (B U C)
A = {-2, -1, 3, 4, 6} and B U C = {-3, -,2, -1, 0, 3, 5, 7, 8}
A − (B U C) = {4, 6}
(vii) A − (B n C)
B n C = {-2, 8}
A = {-2, -1, 3, 4, 6}
A − (B n C) = {-1, 3, 4, 6}
Question 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 :
(i) K U (L n M)
(L n M) = { b, c, d }
K U (L n M) = {a, b, c, d, e, f}
(ii) K n (L U M)
(L U M) = {a, b, c, d, g, h}
K n (L U M) = {a, b, d}
(iii) (K U L) n (K U M)
(K U L) = {a, b, c, d, e, f, g}
(K U M) = {a, b, c , d, e, f, h}
(K U L) n (K U M) = {a, b , c, d , e, f}
(iv) (K n L) U (K n M)
K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}
(K n L) = {b, d}
(K n M) = {a, b, d}
(K n L) U (K n M) = {a, b, d}
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