1.(1) We know that

(a) P(1,1) = 2

(b) P(m+1,n)=P(m,n)+2(m+n)

(c) P(m,n+1)=P(m,n)+2(m+n-1)

Prove or disprove the following formula for any positive integers m and n: P(m,n) = (m+n)(m+n-1) - 2n +2