Question

Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
(i) $\left\{c,d\right\}\subset A$
(ii) $\left\{c,d\right\}\in A$
(iii) $\left\{\left\{c,d\right\}\right\}\subset A$
(iv) $a\in A$
(v) $a\subset A$
(vi) $\left\{a,b,e\right\}\subset A$
(vii) $\left\{a,b,e\right\}\in A$
(viii) $\left\{a,b,c\right\}\subset A$
(ix) $\varphi \in A$
(x) $\left\{\varphi \right\}\subset A$

Answer 1

A = {a, b, {c, d}, e}
(i) False
The correct statement would be $\left\{\left\{c,d\right\}\right\}\subset A$.
(ii) True
(iii) True
(iv) True
(v) False
The correct statement would be {a}⊂ A or a ∈ A.
(vi) True
(vii) False
The correct statement would be $\left\{a,b,e\right\}\subset A$.
(viii) False
The correct statement would be {a, b, c} ⊄ A.
(ix) False
A null set is a subset of every set. Therefore, the correct statement would be $\varphi \subset A$.
(x) False
$\mathrm{\varphi }$ is an empty set; in other words, this set has no element. It is denoted by $\mathrm{\varphi }$. Therefore, the correct statement would be $\varphi \subset A$.