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) $\{1,2,3\} \subset A$
(iii) $\{6,7,8\} \in A$
(iv) $\{\{4,5\}\} \subset A$
(v) $\phi \in A$
(vi) $\phi \subset A$
Solution:
(i) False
If it could be $1 \notin A$, then it would be true .
(ii) False
The correct form would be $\{1,2,3\} \in A$ or $\{\{1,2,3\}\} \subset A$.
(iii) True
(iv) True
(v) False'
A null set is a subset of every set. Therefore, the correct form would be $\phi \subset A$.
(vi) True