Examine whether the following statements are ...

NCERT Class XI Mathematics - Sets - Solutions

Question : 14 of 73

Marks: +1, -0

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}

Solution:

(i) Let A = {a, b} and B = {b, c, a}

Here every element of A is an element of B. ∴ A ⊂ B

Hence, the statement is false.

(ii) Let A = {a, e} and B = {x : x is a vowel in the English alphabet}

∴ B = {a, e, i, o, u}

Here every element of A is an element of B

∴ A ⊂ B. Hence, the statement is true.

(iii) Let A = {1, 2, 3} and B = {1, 3, 5}.

Here 2 ∈ A but 2 ∉ B. ∴ A ⊄ B.

Hence, the statement is false.

(iv) Let A = {a} and B = {a, b, c}.

Here every element of A is an element of B.

∴ A ⊂ B. Hence, the statement is true.

(v) Let A = {a} and B = {a, b, c}.

Here the statement is false because {a} ∉ B.

(vi) Let A = {x : x is an even natural number less than 6}

∴ A = {2, 4}

and B = {x : x is a natural number which divides 36}

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

Here every element of A is an element of B.

∴ A ⊂ B. Hence, the statement is true.

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