**Practice Questions Based on Set Operations :**

Here we are going to see some practice problems based on set operations.

(1) Using the given Venn diagram, write the elements of

(i) A (ii) B (iii) A∪B (iv) A∩B

(v) A–B (vi) B–A (vii) A′ (viii) B′

(ix) U

(2) Find A∪B, A∩B, A–B and B–A for the following sets.

(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}

(iii) A = {x : x ∈N, x ≤ 10} and B = {x : x ∈W, x < 6}

(iv) A= Set of all letters in the word “mathematics” and

B = Set of all letters in the word “geometry”

(3) 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

(4) 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

(5) Find the symmetric difference between the following sets.

(i) P = {2, 3, 5, 7, 11} and Q = {1, 3, 5, 11}

(ii) R = {l, m, n, o, p} and S = {j, l, n, q}

(iii) X = {5, 6, 7} and Y = {5, 7, 9, 10} Solution

(6) Using the set symbols, write down the expressions for the shaded region in the following

(i)

(ii)

(iii)

(7) Let A and B be two overlapping sets and the universal set be U. Draw appropriate Venn diagram for each of the following,

(i) A∪B (ii) A∩B (iii) (A∩B)′ (iv) (B–A)′ (v) A′∪B′ (vi) A′∩B′

(vii) What do you observe from the Venn diagram (iii) and (v)? Solution

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