Let A = {a, b, {c, d}, e}
Let \[ A=\{a,b,\{c,d\},e\} \] Which of the following statements are false and why?
(i) \(\{c,d\} \subset A\)
(ii) \(\{c,d\} \in A\)
(iii) \(\{\{c,d\}\} \subset A\)
(iv) \(a \in A\)
(v) \(a \subset A\)
(vi) \(\{a,b,e\} \subset A\)
(vii) \(\{a,b,e\} \in A\)
(viii) \(\{a,b,c\} \subset A\)
(ix) \(\Phi \in A\)
(x) \(\{0\} \subset A\)
Solution
Elements of \[ A \] are \[ a,\ b,\ \{c,d\},\ e \]
(i) False, because \[ c,d \notin A \]
(ii) True, because \[ \{c,d\} \in A \]
(iii) True, because \[ \{c,d\} \in A \]
(iv) True, because \[ a \in A \]
(v) False, because \[ a \] is not a set.
(vi) True, because all elements \[ a,b,e \] belong to \[ A \]
(vii) False, because \[ \{a,b,e\} \notin A \]
(viii) False, because \[ c \notin A \]
(ix) False, because \[ \Phi \notin A \]
(x) False, because \[ 0 \notin A \]