State whether the following statements are true or false :
(i) 1 ϵ {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.
(i) True , ∵ 1 is an element of the set {1, 2, 3}.
(ii) False, ∵ a is an element and not a subset of the set {b, c,a}.
(iii) False, ∵ {a} is a subset of the set {a, b, c} and not an element.
(iv) True, ∵ repetition is not allowed in a set.
(v) False, ∵ the set {x : x+8 = 8} is the single ton set {0} which is not the null set ϕ }