Prove that `a^p b^ q <((a p+b q)/(p+q))^(p+q)dot`

Using truth table prove that ~p ^^ q -=(p vv q) ^^ ~p

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0

Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove that a/p(q-r) +b/q(r-p) + c/r(p-q)=0 .

If the polynomial (ax^(p)+bx^(q)-3) be divided by (x - a) and (x - b), the remainder in both the cases is (-1). Prove that (a^(p+1)-b^(q+1))/(b^(p-1)-a^(q-1))=ab

In A A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

Prove that q^^~p -=~ (q to p)

Prove that q^^~p -=~ (q to p)

Prove that q^^~p -=~ (q to p)

If a/(q -r) = b/(r-p) = c/(p-q) , then prove that a + b + c = 0 =pa+ qb + rc .

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)