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

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)

If the pth, qth and rth terms of a G.P. are a,b and c, respectively. Prove that a^(q-r)b^(r-p)c^(p-q)=1 .

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

In Fig.9.28, A P" "||" "B Q" "||" "C R . Prove that a r" "(A Q C)" "=" "a r" "(P B R)dot

Using truth table prove that p vee (q wedge r) -= (p vee q) wedge (p vee r)

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 R Q)=1/2a r\ (\ A R C)

In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D P Q) CONSTRUCTION : Join A Cdot

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P\ B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q)