Question

Prove that if four numbers are chosen from the set {l, 2, 3, 4.5.6}, at least one pair of the selected numbers must add up to 7

Answer 1

Explanation:

GIven that:

The set is : {l, 2, 3, 4.5.6}

To Prove that:

If four numbers are to be chosen , at least one pair of the selected numbers must add up to 7

From the data set given, this set has three pairs of number which can add up to 7. These are:

{1, 6} i.e 1 + 6 = 7

{2,5} i.e 2+ 5 = 7

{3,4} i.e 3 + 4 = 7

So, if four number are chosen from the set that contains six numbers, then that the possibility for such to occur is either by selecting two pairs out of the three pairs or one pair and two numbers.

Thus, in both cases, at least one pair of the selected numbers must add up to 7.