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

Question:

Let A = {ab, {cd}, 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) $\{\phi\} \subset A$

Solution:

A = {ab, {cd}, 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 $\phi \subset A$.