# 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

## 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}

**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