Let P = {1, 4,9} and Q= {2,4,6}. Write the elements of `(P nn Q)xx (P uu Q)`. Also find `(P xx Q) nn (Q xx P)`.

If P = {a, b,c } and Q= {r}, form the sets P xx Q and QxxP . Are these two Products equal ?

Let n(P) = 4 and n(Q) = 5. The number of all possible injections from P to Q is :

If P, Q and R are the subsets of a set A, then prove that Rxx(P^(c )uuQ^(c ))^(c )=(RxxP)nn(RxxQ) .

Find the product : (p^2 – q^2) (2p + q)

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_2

Let S_p and S_q be the coefficients of x^p and x^q respectively in (1 + x)^(p+q) , then :

Let P and Q be 3xx3 matrices P ne Q . If P^(3)=Q^(3) and P^(2)Q=Q^(2)P , then determinant of (P^(2)+Q^(2)) is equal to :

Add: p ( p – q), q ( q – r) and r ( r – p)

Find the product : (-10/3 pq^3)xx(6/5 p^3q)