If π΄ and B are finite sets which are subsets of π. Establish a formula for π(π΄ βͺ π΅) in terms of π(π΄), π(π΅) and π(π΄ β© π΅). Hence or otherwise deduce a formula for a particular case where A and B are disjoint?
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We have that
because if we writeΒ Β we are counting each element ofΒ Β twice.
Β andΒ Β are disjoint if they have no elements in common. That is,Β Β . Therefore, substituting to the above formula we deduce that