Lemma 3.4.9 Let \(X\) be a set. Then the set $$ \{Y:Y\text{ is a subset of }X\} $$ is a set.
\(Proof\). See Exercies 3.4.6.
Lemma 3.4.9 Let \(X\) be a set. Then the set $$ \{Y:Y\text{ is a subset of }X\} $$ is a set.
\(Proof\). See Exercies 3.4.6.
Prove Lemma 3.4.9. (Hint: start with the set \(\{0,1\}^X\) and apply the replacement axiom, replacing each function \(f\) with the object \(f^{-1}(\{1\})\).)
See also Exercise 3.5.11.
Exercise 3.4.6. Prove Lemma 3.4.9. (Hint: start with the set \(\{0,1\}^X\) and apply the replacement axiom, replacing each function \(f\) with the object \(f^{-1}(\{1\})\).)\\ See also Exercise 3.5.11.