Answer to Question #135019 in Discrete Mathematics for Promise Omiponle

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, because $x$ belongs to the given set of elements.

(b) false, because {$x$} is a subset of given subset, not a proper subset.

(c) false, because $x$ is an element, not {$x$}.

(d) true, because in this case {$x$} is an element contained in the given set.

(e) true, because here $\phi$ is an element in the set. So, {$\phi$} is the proper subset of the given set.

(f) true, because $\phi$ is a proper subset of all the sets.

(g) true, because $\phi$ is a proper subset of all sets.