Let `A = {a_(1), b_(1), c_(1)}` and `B = {a_(2), b_(2)}`
(i) `A xx B`
(ii) `B xx B`

Let A = {5, 10, 15} and B = {a_(1), a_(2), a_(3)} . Represent (i) A xx B (ii) B xx A

Let A = {p, q, r} and B = {1, 2}. Represent (i) A xx B (ii) B xx B

Let A = {a_(1), b_(1), c_(1)} , B = {r, t}. Find the number of relations from A to B.

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

Let A= {1, 2, 3} , B = {3, 4} and C = {4, 5, 6} . Find(i) A xx(B nnC) (ii) (A xxB) nn(A xxC) (iii) A xx(B uuC) (iv) (A xxB) uu(A xxC)

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

If two equation a_(1) x^(2) + b_(1) x + c_(1) = 0 and, a_(2) x^(2) + b_(2) x + c_(2) = 0 have a common root, then the value of (a_(1) b_(2) - a_(2) b_(1)) (b_(1) c_(2) - b_(2) c_(1)) , is

Find the condition for two lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 to be (i) parallel (ii) perpendicular

If a_(1) x^(3) + b_(1)x^(2) + c_(1)x + d_(1) = 0 and a_(2)x^(3) + b_(2)x^(2) + c_(2)x + d_(2) = 0 a pair of repeated roots common, then prove that |{:(3a_(1)", "2b_(1) ", "c_(1)),(3a_(2)", " 2b_(2)", "c_(2)),(a_(2)""b_(1)- a_(1)b_(2)", "c_(2)a_(1)-c_(2)a_(1)", "d_(1)a_(2)-d_(2)a_(1)):}|=0

The value of the determinant Delta = |(1 + a_(1) b_(1),1 + a_(1) b_(2),1 + a_(1) b_(3)),(1 + a_(2) b_(1),1 + a_(2) b_(2),1 + a_(2) b_(3)),(1 + a_(3) b_(1) ,1 + a_(3) b_(2),1 + a_(3) b_(3))| , is