If 𝐴 and B are finite sets which are subsets of 𝑈. Establish a formula for 𝑛(𝐴 ∪ 𝐵) in terms of 𝑛(𝐴), 𝑛(𝐵) and 𝑛(𝐴 ∩ 𝐵). 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 write we are counting each element of twice.
and are disjoint if they have no elements in common. That is, . Therefore, substituting to the above formula we deduce that