Addition theorem on sets [ n(AUB) = n(A)+n(B) - n(A∩B) ] formula

 1) Addition theorem of two sets

Here we notice that n(A) + n(b) => 5+6 = 11 this is so because there are some elements that are common to both A and B  but in AUB we count the common elements only "one" time , so n(AUB) =9 

Hence we infer that n(AUB) = n(A) + n(b) - n(A∩B), 

1,2,3,4,5 is already counted in n(A) and therefore should be subtracted when counting n(B) or else it will be counted 2 times.

2) Addition theorem on 3 sets and n sets:

3) Some Problems on Addition theorem: