Question

State whether the following statements are true or false :

(i) 1 $ϵ$ {1, 2, 3} (ii) a $\subset$ {b, c, a}

(iii) {a} $\subset$ {a, b, c}

(iv) {a, b} = {a,a,b,b, a}

(v) The set {x : x +8=8} is the null set.

Answer 1

(i) True , $\because$ 1 is an element of the set {1, 2, 3}.

(ii) False, $\because$ a is an element and not a subset of the set {b, c,a}.

(iii) False, $\because$ {a} is a subset of the set {a, b, c} and not an element.

(iv) True, $\because$ repetition is not allowed in a set.

(v) False, $\because$ the set {x : x+8 = 8} is the single ton set {0} which is not the null set $\varphi$ }