Solution to If 𝐴 and B are finite sets which are subsets of π‘ˆ. Establish a formula … - Sikademy
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Archangel Macsika

If 𝐴 and B are finite sets which are subsets of π‘ˆ. Establish a formula for 𝑛(𝐴 βˆͺ 𝐡) in terms of 𝑛(𝐴), 𝑛(𝐡) and 𝑛(𝐴 ∩ 𝐡). Hence or otherwise deduce a formula for a particular case where A and B are disjoint?

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We have that


n(A\cup B)=n(A)+n(B)-n(A\cap B)

because if we writeΒ n(A)+n(B)Β we are counting each element ofΒ A\cap BΒ twice.

AΒ andΒ BΒ are disjoint if they have no elements in common. That is,Β n(A\cap B)=0Β . Therefore, substituting to the above formula we deduce that


n(A\cup B)=n(A)+n(B).

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