- #1

bubblescript

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## Homework Statement

If ##\mathcal{F}## is a family of sets and ##A \in \mathcal{F}##, then ##A \subseteq \cup \mathcal{F}##.

## Homework Equations

##A \subseteq \cup \mathcal{F}## is equivalent to ##\forall x(x \in A \rightarrow \exists B(B \in \mathcal{F} \rightarrow x \in B))##.

## The Attempt at a Solution

Suppose ##A \in \mathcal{F}##. Let ##x## be arbitrary and suppose ##x \in A##. Clearly ##\exists B \in \mathcal{F}## is true if we say that ##B=A##. Therefore we conclude that if ##A \in \mathcal{F}##, then ##A \subseteq \cup \mathcal{F}##.