NCERT Class XI Mathematics - Sets - Solutions

Question : 14

Total: 73

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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