**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}**

Answer

**(i) False.**

All element of {a, b} lies in set {b, c, a}. So {a, b} ⊂ {b, c, a}

Hence given statement is false.

**(ii) True.**

‘a’ and ‘e’ both are vowels of the English alphabet.

So that , {a, e} ⊂ {x: x is a vowel in the English alphabet}.

Hence given statement is true.

**(iii) False.**

‘2’ lies in set {1, 2, 3} but don’t lies in set {1, 3, 5}

So that, {1, 2, 3} ⊄ {1, 3, 5}.

Hence, given statement is false.

**(iv) True.**

All elements of set {a} are also an element of set {a, b, c}.

So that, {a} ⊂ {a. b, c}

Hence, given statement is true.

**(v) False.**

{a} is not an element of set {a, b, c}.

So that correct statement will a ∈ {a. b, c}

Hence, given statement is False.

**(vi) True.**

Even natural numbers less than 6 are 2 and 4.

Natural numbers which are divided by 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

2 and 4 both lies in set { 1, 2, 3, 4, 6, 9, 12, 18, 36}.

So that {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}

Hence, given statement is true.

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