Sets

Which of the following sets are finite or infinite 

(i) The set of months of a year 

(ii) {1, 2, 3 …} 

(iii) {1, 2, 3 … 99, 100} 

(iv) The set of positive integers greater than 100 (v) The set of prime numbers less than 99 

Examine whether the following statements are true or false: 

(i) {a, b} ⊄ {b, c, a} 

(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet} 

(iii) {1, 2, 3} ⊂{1, 3, 5} 

(iv) {a} ⊂ {a. b, c} (v) {a} ∈ (a, b, c) 

(vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36} 

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 

Decide, among the following sets, which sets are subsets of one and another: 

A = {x: x ∈ R and x satisfy x2 – 8x + 12 = 0}, 

B = {2, 4, 6}, 

C = {2, 4, 6, 8…}, 

D = {6}. 

Find the union of each of the following pairs 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