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 $F \subseteq \wp(B)$.
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](https://matchmaticians.com/storage/user/100977/thumb/matchmaticians-ee0kis-file-1-avatar-512.jpg)
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
- 459 views
- $5.00
Related Questions
- Fix any errors in my proof (beginner)
- Discrete Structures - Proving a statement true
- Proof through inclusion (A∆B) ∪ A = A ∪ B
- Operational Research probabilistic models
- Topic: Large deviations, in particular: Sanov's theorem
- Suppose that $(ab)^3 = a^3 b^3$ for all $a, b \in G$. Prove that G must be an abelian goup [Group Theory].
- Combinatorics proof by induction
- $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} $