Answer to Question #166723 in Discrete Mathematics for Aaron

Question

  Determine whether each of the following statements is true or false. State the reason.

i) ∅ ∉ ∅

ii) ∅ ⊆ ∅

iii) {∅} ⊆ ∅

Answer 1

$i)\forall{a}(a\notin\varnothing)\Rightarrow\varnothing\notin\varnothing\text{ True}$

$ii)\forall{a}(\varnothing\sube{a})\Rightarrow\varnothing\sube\varnothing\text{ True}$

$iii)\varnothing\text{ has zero elements, and }\{\varnothing \}\text{ has one element.}$ $\varnothing\sube\varnothing;$

$\{\varnothing \}\sube\varnothing\text{ is False}$