# Fix any errors in my proof (beginnner)

**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 $F \subseteq \wp(B)$.

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

The answer is accepted.

- answered
- 100 views
- $5.00

### Related Questions

- Discrete Structures - Proving a statement false by proving the negation to be true
- Induction proof for an algorithm. Introductory level discrete math course. See attachment for details
- Proof through inclusion (A∆B) ∪ A = A ∪ B
- Let $f\in C (\mathbb{R})$ and $f_n=\frac{1}{n}\sum\limits_{k=0}^{n-1} f(x+\frac{k}{n})$. Prove that $f_n$ converges uniformly on every finite interval.
- Fix any errors in my proof (beginner)
- $Use induction to prove that for any natural n the following holds: 1\bullet2+2\bullet 3+...+(n-1)\bullet n=\frac{(n-1)n(n+1)}{3} $
- Fix any errors in my proof (beginner)
- proof by induction