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.