Question

5. If n(AUB)= 10, n(B-A)=8 and n( ∩ )=3, find (i) n(b)
(ii) n(A)

Answer 1

Answer:

These type of problems become a lot easy when you keep Venn diagram in your mind.

Imagine two sets A and B with n(A)>n(B) . They can be totally disjoint, leading to no common elements. Therefore having maximum elements in union which is n(A)+n(B) .

In other case, where few elements are common, their union will lead to fewer number of elements as some elements are common and won't be repeated twice.

But if one of the set is a subset of the other (in this case it would be B⊂A ), then their union will give the minimum number of elements possible (which will be the number of elements of the superset, in this case set A).

∴ your answer would be n(A)=10