Question

Two sets, A and B, are such that n(A U B) =10 and n(A) =4. Calculate the smallest possible value of n(B) and the largest possible value of n(B).

Answer 1

Since the n of the union of A and B is 10 and n of just A is 4, we can say that the function n is the 'max' function, i.e. results in the largest possible value of the input. For function n, when the input is A U B, result is 10. That means that when sets A and B are combined, the largest possible value in the union is 10. But in A alone, the largest value is 4.

Since the largest element in A is 4, and the largest element of A U B is 10, we can say that the largest element of B is 10. Since the union of 2 sets is just combining all the elements of two sets, we can say that if set A has the largest value 4 and set be has the largest value 10, then set A can still have any number of values all less than 4 and set B can have any number of values all of which are less than 10.

This implies that n(B) = max(B) = 10

Although since the original question doesn't state the type of numbers in the sets (negative, positive, non-negative, non-positive, non-zero, integers or real numbers) then the values of set A less than 4 and values of set B less than 10 could really be any value that satisfies the condition min(A) E (-infinity, 4) and min(B) E (-infinity, 10).

Answer 2

Thanks a million! I totally understand it :)