Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?
(i) $\{c, d\} \subset A$
(ii) $\{c, d\} \in A$
(iii) $\{\{c, d\}\} \subset A$
(iv) $a \in A$
(v) $a \subset A$
(vi) $\{a, b, e\} \subset A$
(vii) $\{a, b, e\} \in A$
(viii) $\{a, b, c\} \subset A$
(ix) $\phi \in A$
(x) $\{\phi\} \subset A$
A = {a, b, {c, d}, e}
(i) False
The correct statement would be $\{\{c, d\}\} \subset A$.
(ii) True
(iii) True
(iv) True
(v) False
The correct statement would be $\{a\} \subset A$ or $a \in A$.
(vi) True
(vii) False
The correct statement would be $\{a, b, e\} \subset A$.
(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 $\phi \subset A$.
(x) False
$\phi$ is an empty set; in other words, this set has no element. It is denoted by $\phi$. Therefore, the correct statement would be $\phi \subset A$.