Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}.

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) $\phi \subset A$
ϕ⊂A">ϕ⊂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

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