If P={1,2}, form the set `P xx P xx P`

If P={a,b,c} and Q={r}, form the sets P xx Q and Q xx P . Check if the products are equal or not?

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi

p(x) =x +2. Find p(1), p (2),p (-1) and p (-2). Which among 1,2,-1 and -2 becomes the 0 of p (x) ?

If P= {x: x lt 3, x in N}, Q = {x : x le 2, x in W} then find (P uu Q) xx (P nn Q) , where W is the set of whole numbers.

Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, 4, ....., n}. Find P(r le p//s le p) , where p in S.

If p ,q , in {1,2,3,4}, then find the number of equations of the form p x^2+q x+1=0 having real roots.

If (1+3p)/3,(1-p)/1,(1-2p)/2 are the probabilities of 3 mutually exclusive events then find the set of all values of p.

If p(t)=t^(3)-1 , find the values of p(1),p(-1),p(0),p(2),p(-2) .

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B ) ? Justify your answer.