Family of subsets

**tigergirl** · April 27th 2010, 12:46 PM

Prove: If $A \rightarrow B$ is a function and { $C_\lambda \mid \lambda \epsilon \Lambda$ } is a family of subsets of A, then $f ( \bigcup_{\lambda \epsilon \Lambda} C_\lambda) = \bigcup_{\lambda \epsilon \Lambda} f (C_\lambda)$

**Plato** · April 27th 2010, 01:26 PM

Originally Posted by tigergirl

Prove: If $A \rightarrow B$ is a function and { $C_\lambda \mid \lambda \epsilon \Lambda$ } is a family of subsets of A, then $f ( \bigcup_{\lambda \epsilon \Lambda} C_\lambda) = \bigcup_{\lambda \epsilon \Lambda} f (C_\lambda)$

You need to show some of your own effort.
Answer these two questions:
1) What does it mean to say $s \in f\left( {\bigcup\limits_{\lambda \in \Lambda } {C_\lambda } } \right)?$

2) What does it mean to say $t \in \bigcup\limits_{\lambda \in \Lambda } {f(C_\lambda )}?$

**emakarov** · April 27th 2010, 01:27 PM

Basically, the problem is to show that $f(C_1\cup C_2)=f(C_1)\cup f(C_2)$ . Both inclusions are pretty obvious. I don't think the extension to infinite families $\Lambda$ (from $\Lambda=\{1,2\}$ just considered) presents any problems.

Thread: Family of subsets

LinkBack

Thread Tools

Display

Family of subsets

Similar Math Help Forum Discussions

Family of subsets

Family Sets

Family functions

Family Gathering

Family of five

Search Tags