$f(A \\cup B) = f(A) \\cup f(B)$ - Mathematics Stack Exchange
2019年4月7日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Does $f(A \\cup B) = f(A) \\cup f(B)$? imply that $f^{-1}(A \\cup B ...
2017年10月22日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
functions - Maps - question about $f(A \cup B)=f(A) \cup f(B)$ and …
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functions - How would I show that $f(A \cup B) = f(A) \cup f(B ...
2016年10月21日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Show that $f^{-1}(A \\cup B) = f^{-1}(A) \\cup f^{-1}(B)$
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elementary set theory - About proving $f(S \cup T) = f(S) \cup f(T ...
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Proving $f(C\\cap D)=f(C)\\cap f(D)$ and $f(C\\cup D)=f(C)\\cup …
2015年1月6日 · In general you seem to fail to distinguish between, say, $2$ and $\{2\}$. Those are quite different things -- one of them is a number, the other is a set that contains a number.
Method for proving $ f^{-1}(G \\cup H) = f^{-1}(G)\\cup f^{-1}(H)
Without loss of generality, suppose $ y \in G $. Then $ x \in f^{-1}(G) $. So $ x \in f^{-1}(G) \cup f^{-1}(H) $. Assume $ x \in f^{-1}(G) \cup f^{-1}(H) $. Then $ x\in f^{-1}(G) $ or $ x\in f^{-1}(H) $. Without loss of generality, suppose that $ x\in f^{-1}(G) $. So there exists some $ y \in G $ such that $ f^{-1}(y) = x $. Since $ y \in G ...
graph theory - Is $F \cup E(F')$ a forest? How show?
2022年3月25日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
calculus - Show that if $f$ and $g$ are surjective, then $f\cup g$ is ...
2018年9月26日 · In the text of 'Introduction to Mathematical structures and Proofs', by Larry Garstein; there are below sub-problems as part of Q. 14 in Ex.#3.3, as shown here. Have taken a few questions below: ...