Exercise 1.3: Set Operations

Exercise 1.3

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′)′

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′)′

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}

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

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)?