Question

Suppose n(X) = 26 and n(Y) = 13.
What is the minimum number of elements X ∪ Y can have?

Answer 1

Explanation:

the minimum is when we unite X and Y (add Y to X) and there is no increase in the number of elements : that means that all elements of Y were already elements of X.

therefore, when both sets fully overlap.

and so, the minimum number of elements of X ∪ Y is the number of elements of the larger set : X = 26

Answer 2

26

Explanation:

To find the minimum number of elements in the union of sets X and Y, we can consider the best-case scenario where there is maximum overlap between the two sets.

In the best-case scenario, if X and Y have some common elements, the minimum number of elements in X ∪ Y would be equal to the larger of the two sets.

Given n(X) = 26 and n(Y) = 13, the minimum number of elements in X ∪ Y would be max(n(X),n(Y) = max(26, 13) = 26.

So, the minimum number of elements in X ∪ Y is 26.