Question

Which of the following statements are correct ? Write a correct form of each of the incorrect statements.

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

(ii) {a} $ϵ$ {a, b, c}

(iii) a $ϵ$ {(a), b}

(iv) {a} $\subset$ {(a), b}

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

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

(vii) $\varphi ϵ$ {a, b}

(viii) $\varphi \subset$ {a, b, c}

(ix) {x : x +3 = 3} = $\varphi$

Answer 1

(i) False.

The correct statement is a $ϵ$ {a, b, c}

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

The correct form is {a} $\subset$ {a, b, c}

(iii) False, $\because$ a is not an element of {{a}, b} The correct form is {a} $ϵ$ {{a}, b}

(iv) False, $\because$ {a} is not a subset of {{a}, b} hence it cannot be contained in it.

The correct form is {a} $ϵ$ {{a}, b}. Another correct form could be {{a}} $\subset$ {{a}, b}.

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

The correct form is {b,c} $ϵ$ {a, {b, c}}.

(vi) False, $\because$ {a, b} is not a subset of {a, {b, c}}.

The correct form is {a, b} $⊈$ {a, } {b,c }}.

(vii) False, $\because$ $\varphi$ is not an element of {a, b}.

The correct form is $\varphi$ $\subset${a, b}

(viii) True. $\because$ empty set $\varphi$ is a subset of every set.

(ix) False, $\because$ {x : x +3 = 3} = {x : x = 0} = {0}

The correct form is {x :x +3 = 3} $\ne \varphi$.