State whether the following statements are true or false:
Question:

State whether the following statements are true or false:

(i) $1 \in\{1,2,3\}$

(ii) $a \subset\{b, c, a\}$

(iii) $\{a\} \in\{a, b, c\}$

(iv) $\{a, b\}=\{a, a, b, b, a\}$

(v) The set $\{x ; x+8=8\}$ is the null set.

Solution:

(i) True

(ii) False

It should be written as $\{a\} \subset\{b, c, a\}$ or $a \in\{b, c, a\}$.

(iii) False

It should be written as $\{a\} \subset\{b, c, a\}$ or $a \in\{b, c, a\}$.

(iv) True

(v) False

The element of the set $\{x ; x+8=8\}$ is $\{0\}$. Therefore, it is not an empty or null set.