Question

Determine whether the statements below are true or false.
(a) x ϵ {x}
(b) {x} ⊆ {x}
(c) {x} ϵ {x}
(d) {x} ϵ {{x}}
(e) {Ø} ⊆ {Ø,,{Ø}}
(f) Ø ⊆ {x}
(g) Ø ⊆ {x}

Answer 1

a) true, $x$ is an element of the set $\{x\}$ ;

b) true, the set $\{x\}$ is a subset of itself;

c) false, $x$ is an element of $\{x\}$ , but the set $\{x\}$ is not an element of $\{x\}$ ;

d) true, the set $\{x\}$ is an element of the set $\{\{x\}\}$ ;

e) true, the set $\{Ø\}$ is an element of the set $\{Ø,\{Ø\}\}$ ;

f) true, g) true, the empty set $Ø$ is a subset of any set.