Let A = {a, b, {c, d}, e}. Which of the following statements are false and why?

Solution:

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 $\phi \subset A$.