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:

We will see what are ⊂ and ⊄.

⊂ means "a subset of".

If we write A ⊂ B, then we read it as "A is a subset of B" and it means that all the elements of A are present in B.

⊄ means "NOT a subset of".

If we write A ⊄ B, then we read it as "A is NOT a subset of B" and it means that there are some elements of A that are NOT present in B.

Thus,

(i) { a, b } ⊄ { b, c, a } is FALSE as { a, b } ⊂ { b, c, a }

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

(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 } is FALSE as { 1, 2, 3 } ⊄ { 1, 3, 5 }

(iv) { a } ⊂ { a, b, c } is TRUE.

(v) { a } ∈ { a, b, c } is FALSE.

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

{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} and

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

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.3 Question 2

Summary:

(i) { a, b } ⊄ { b, c, a } is False

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

(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 } is False

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

(v) { a } ∈ { a, b, c } is False.

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

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

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