Let A = {{1,2,3},{4,5},{6,7,8}}
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
Elements of \[ A \] are \[ \{1,2,3\},\ \{4,5\},\ \{6,7,8\} \]
(i) False, because \[ 1 \notin A \]
(ii) False, because \[ 1,2,3 \] are not elements of \[ A \]
(iii) True, because \[ \{6,7,8\} \in A \]
(iv) True, because \[ \{4,5\} \in A \]
(v) False, because \[ \Phi \notin A \]
(vi) True, because the empty set is a subset of every set.