Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why? 

(i) {3, 4}⊂ A 

(ii) {3, 4}}∈ A

(iii) {{3, 4}}⊂ A 

(iv) 1∈ A 

(v) 1⊂ A 

(vi) {1, 2, 5} ⊂ A 

(vii) {1, 2, 5} ∈ A 

 (viii) {1, 2, 3} ⊂ A 

(ix) Φ ∈ A 

(x) Φ ⊂ A 

(xi) {Φ} ⊂ A 

Which of the following pairs of sets are disjoint 

(i) {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6} 

(ii) {a, e, i, o, u} and {c, d, e, f} 

(iii) {x: x is an even integer} and {x: x is an odd integer} 

Write down all the subsets of the following sets: 

(i) {a} 

(ii) {a, b} 

(iii) {1, 2, 3} 

(iv) Φ 

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find 

(i) A ∩ B 

(ii) A ∩ C 

(iii) A ∩ D 

(iv) B ∩ C 

(v) B ∩ D 

(vi) C ∩ D 

How many elements has P(A), if A = Φ? 

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find 

(i) A ∩ B 

(ii) B ∩ C 

(iii) A ∩ C ∩ D 

(iv) A ∩ C (v) B ∩ D 

(vi) A ∩ (B C) 

(vii) A ∩ D 

(viii)A ∩ (B D) 

(ix) (A ∩ B) ∩ (B C) 

(x) (A D) ∩ (B C) 

Find the intersection of each pair of sets: 

(i) X = {1, 3, 5} Y = {1, 2, 3} 

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

(iii) A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6} 

(iv) A = {x: x is a natural number and 1 < x ≤ 6} B = {x: x is a natural number and 6 < x < 10} 

(v) A = {1, 2, 3}, B = Φ 

Write the following as intervals: 

(i) {x: x ∈ R, –4 < x ≤ 6} 

(ii) {x: x ∈ R, –12 < x < –10} 

(iii) {x: x ∈ R, 0 ≤ x < 7} 

(iv) {x: x ∈ R, 3 ≤ x ≤ 4} 

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find 

(i) A ∪ B 

(ii) A UC 

(iii) B ∪ C 

(iv) B ∪ D 

(v) A ∪ B ∪ C 

(vi) A ∪ B ∪ D 

(vii) B ∪ C ∪ D