Question

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} 

Answer 1

(i) False. Each element of {a, b} is also an element of {b, c, a}. 

(ii) True. a, e are two vowels of the English alphabet. 

(iii) False. 2∈{1, 2, 3}; however, 2∉{1, 3, 5} 

(iv) True. Each element of {a} is also an element of {a, b, c}. 

(v) False. The elements of {a, b, c} are a, b, c. Therefore, {a}⊂{a, b, c} 

(vi) True. {x:x is an even natural number less than 6} = {2, 4} 

{x:x is a natural number which divides 36}= {1, 2, 3, 4, 6, 9, 12, 18, 36}