Question

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}. Determine which of the following is true or false:
(i) $1\in A$
(ii) $\left\{1,2,3\right\}\subset A$
(iii) $\left\{6,7,8\right\}\in A$
(iv) $\left\{\left\{4,5\right\}\right\}\subset A$
(v) $\varphi \in A$
(vi) $\varphi \subset A$

Answer 1

(i) False
If it could be 1$\notin$A , then it would be true .

(ii) False
The correct form would be $\left\{1,2,3\right\}\in A\mathrm{or}\left\{\left\{1,2,3\right\}\right\}\subset A$.

(iii) True

(iv) True

(v) False
A null set is a subset of every set. Therefore, the correct form would be $\mathrm{\varphi }\subset A$.

(vi) True