- #1
Mr Davis 97
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Homework Statement
Prove that if ##A \subseteq B##, then ##\bigcup A \subseteq \bigcup B##.
Homework Equations
The Attempt at a Solution
This is a simple problem, but I just want to make sure I am writing out the proof correctly:
Suppose that ##A \subseteq B##. We want to show that ##\bigcup A \subseteq \bigcup B##. So consider any ##t \in \bigcup A##. This means that ##t## is a member of one of the sets contained in ##A##. But ##A \subseteq B##, so ##t## is also a member of one of the sets contained in ##B##, which implies ##t \in \bigcup B##.
Is there any way I could improve the proof? I just want to make sure I'm doing these right.
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