When n = 2, there are 1 elements as a subset of 2.

Suppose that for any set with n elements, there are n(n- 1)/2 subsets of size 2, and n ≤ m.

Then for a set with m+ 1 elements, it must be proved that it satisfies the form of (m+1) (m+1-1)/2.

Regardless of m+ 1, m elements have m(m- 1)/2 subsets of size 2.

Now m elements correspond to the added m+ 1 elements, and m subsets of size 2 can be generated.

A * * * is m+m(m- 1)/2 subsets of size 2,

M+m (m-1)/2 = (2m+m2-m)/2 = (m2+m)/2 = (m+1) m/2 satisfies the form.