1. ## discrete mate

4. Let
A, B be finite sets. Recall that |A B| = |A| + |B| - |A B|. Find a similar formula
for |A
B C| using formal proof.

thank q for who helping.......

2. Originally Posted by cclia
4. Let
A, B be finite sets. Recall that |A B| = |A| + |B| - |A B|. Find a similar formula
for |A
B C| using formal proof.

thank q for who helping.......

Hello,

$|A \cup B \cup C|=|D \cup C|$

So consider $A \cup B=D$

Now use the formula you're given :

$|D \cup C|=|D|+|C|-|C \cap D|$

This gives $=|A \cup B|+|C|-|(A \cup B) \cap C|$

$=|A|+|B|-|A \cap B|+|C|-|(A \cap C) \cup (B \cap C)|$

$=|A|+|B|+|C|-|A \cap B|-\left(|A \cap C|+|B \cap C|-|A \cap C \cap B \cap C| \right)$

$=|A|+|B|+|C|-|A \cap B|-|A \cap C|-|B \cap C|+|A \cap B \cap C|$