Thread: Family of sets.

For the following four properties of set algebra, write down what they reduce to for a family of just two sets;

$\displaystyle B \cap \bigcup_{\lambda \in \Lambda} A_{\lambda} = \bigcup_{\lambda \in \Lambda}(B \cap A_{\lambda})$

$\displaystyle B \cup \bigcap_{\lambda \in \Lambda} A_{\lambda} = \bigcap_{\lambda \in \Lambda}(B \cup A_{\lambda})$

$\displaystyle \left(\bigcup_{\lambda \in \Lambda}A_{\lambda}\right)' = \bigcap_{\lambda \in \Lambda}A'_{\lambda}$

$\displaystyle \left(\bigcap_{\lambda \in \Lambda}A_{\lambda}\right)' = \bigcup_{\lambda \in \Lambda}A'_{\lambda}$

I'm not entirely sure what the $\displaystyle \bigcap \bigcup$ symbols mean so if my workings wrong that's probably why. I don't want the answer, just someone to say whether this is right so far.

For the first two... It reduces to;

$\displaystyle B \cap (A_1 \cup A_2) = (B \cap A_1)\cup(B \cap A_2)$

And

$\displaystyle B \cup (A_1 \cap A_2) = (B \cup A_1)\cap(B \cup A_2)$

Right so far?

Originally Posted by Deadstar

Right so far?

Yes, right so far!