Question 1 :
If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets.
(i) A′ (ii) B′ (iii) A′∪B′ (iv) A′∩B′ (v) (A∪B)′
(vi) (A∩B)′ (vii) (A′)′ (viii) (B′)′
Solution :
(i) A' = {a, c, e, g}
(ii) B' = {b, c, f, g}
(iii) A′∪B′ = { a, b, c, e, g }
(iv) A′∩B′ = { c, g }
(v) (A∪B)′
To find (A∪B)′, first we have to find A U B
A U B = {a, b, d, e, f, h}
(A U B)' = {c, g}
(vi) (A∩B)′ = {a, b, c, e, g }
(vii) (A′)′
A = {b, d, f, h}
(viii) (B′)′
B = {a, d, e, h}
Question 2 :
Let U = {0, 1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.
(i) A′ (ii) B′ (iii) A′∪B′ (iv)A′∩B′ ( v)(A∪B)′
(vi) (A∩B)′ (vii) (A′)′ (viii) (B′)′
Solution :
(i) A' = {0, 2, 4, 6}
(ii) B' = {1, 4, 6}
(iii) A′∪B′ = {0, 1, 2, 4, 6 }
(iv) A′∩B′ = {4, 6}
(v) (A∪B)′
To find (A∪B)′, first we have to find A U B
A U B = {0, 1, 2, 3, 5, 7}
(A U B)' = {4, 6}
(vi) (A∩B)′ = {0, 1, 2, 4, 6 }
(vii) (A′)′
{1, 3, 5, 7}
(viii) (B′)′
B = {0, 2, 3, 5, 7}
Question 3 :
Find the symmetric difference between the following sets.
(i) P = {2, 3, 5, 7, 11} and Q = {1, 3, 5, 11}
Solution :
P Δ Q = (P - Q) U (Q - P)
P - Q = {2, 7}
Q - P = {1, 11}
(P - Q) U (Q - P) = {1, 2, 7, 11}
Hence the value of P Δ Q is {1, 2, 7, 11}
(ii) R = {l, m, n, o, p} and S = {j, l, n, q}
Solution :
R Δ S = (R - S) U (S - R)
R - S = {m, o , p}
S - R = {j, q}
(R - S) U (S - R) = {j, m, o, p, q}
Hence the value of R Δ S is {j, m, o, p, q}.
(iii) X = {5, 6, 7} and Y = {5, 7, 9, 10}
Solution :
X Δ Y = (X - Y) U (Y - X)
X - Y = {6}
Y - X = {9, 10}
(X - Y) U (Y - X) = {6, 9, 10}
Hence the value of X Δ Y is {6, 9, 10}.
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