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State whether the following statements are true or false:
(i) 1 ∈ { 1,2,3}
(ii) a ⊂ {b,c,a}
(iii) {a} ∈ {a,b,c}
(iv) {a, b} = {a, a, b, b, a}
(v) The set {x: x + 8 = 8} is the null set.

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(i) True

Since, 1 belongs to the given set {1, 2, 3} as it is present in it.

(ii) False

Here, a is an element and not a subset of a set {b, c, a}

(iii) False

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

(iv) True

Since, we do not have repeat same elements in a given set.

(v) False

Given as, x + 8 = 8

i.e. x = 0

Therefore, the given set is a single ton set {0}. Here, it is not a null set.

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