If A and B be two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in A ∪ B ? Find, also the maximum number of elements in A ∪ B ?
A has 3 elements and B has 6 elements.
will be minimum when A is the subset of B.
hence minimum number of elements in is 6.
will be maximum when A and B are disjoint sets.
hence maximum number of elements in is 3+6=9
we know that a union of sets contains all the elements of both the sets. the common elements are mentioned only once. for the minimum number of elements all the elements in A are also present in B. so the total elements in A U B=6. for max elements the elements of A are not present inB therefore there will be 3+6=9 elements.
hope that helps!!