Question

Examine the following statements : 

(i) {a, b} ⊂ {b, a, c] 

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

(iii) {1, 2, 3} ⊄ {1, 3, 2, 5} 

(iv) {x : x is an even natural number less than 6} ⊄ {x : x is a natural number which divide 36}

Answer 1

(i) {a, b} ⊂ {b, a, c} 

Elements of first set (a, b) is present in second set.

Hence, the statement is true. 

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

Tabular form of seconds set is {a, e, i, o, u}

Elements of first set (a, e is present is second set.

Hence, the statement is true. 

(iii) {1, 2, 3} ⊄ {1, 3, 2, 5}

Elements of first set is also the elements of seconds set.

Hence, the statement is false. 

(iv) {x : x is an even natural number less then 6} ⊂ (x : x is a natural number which divide 36} 

{2, 4} ⊂ {1, 2, 3, 4, 6, 9, 12, 18, 36}

Hence, the statement is true.