Given two sets A: {15, 16, 17, 18, 19} and B: {8, 9, 10, 11, 12, 13, 14}. If C= A + B, then how many distinct values are possible for C?
12?
Well notice that the set A + B is neither included in the set A nor in the set B. Therefore the number of combinations are 5 (the number of elements in A) + 7 (the number of elements in B) = 12.
That is because the smallest element in A is 15, and in B it is 8. Yet, 15 + 8 = 23 which is greater than the greatest element in A or B. Do it the other way too, and you have a proof (I think ).