Fix any errors in my proof (beginnner)
Fix any errors in correctness, structure, etc.
Theorem. Suppose $B$ is a set and $F$ is a family of sets. If $\bigcup F \subseteq B$, then $F \subseteq \wp(B)$.
Proof. Suppose $\bigcup F \subseteq B$. Let $y$ be an arbitrary element such that $y \in F$. Let x be an arbitrary element such that $x \in y$. It follows that $x \in \bigcup F$ and that $x \in B$. Because $\forall x(x \in y \implies x \in B)$, it follows that $y \subseteq B$ and by definition of powerset $y \in \wp(B)$. Because $\forall y(y \in F \implies y \in \wp (B)$), we can conclude that $F \subseteq \wp(B)$.
Faithalone
361
Answer
Answers can only be viewed under the following conditions:
 The questioner was satisfied with and accepted the answer, or
 The answer was evaluated as being 100% correct by the judge.
Alessandro Iraci
1.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
 answered
 407 views
 $5.00
Related Questions
 Proof through inclusion (A∆B) ∪ A = A ∪ B
 Induction proof for an algorithm. Introductory level discrete math course. See attachment for details
 Suppose that $(ab)^3 = a^3 b^3$ for all $a, b \in G$. Prove that G must be an abelian goup [Group Theory].

Math Proofs: "An alternative notation is sometimes used for the union or intersection of an indexed family of sets."
 Given $f(x)  f(y) \leq Mxy^2$ , prove that f is constant.
 Let $f\in C (\mathbb{R})$ and $f_n=\frac{1}{n}\sum\limits_{k=0}^{n1} f(x+\frac{k}{n})$. Prove that $f_n$ converges uniformly on every finite interval.
 Discrete Structures  Proving a statement true
 Operational Research probabilistic models