Let X = {Ram, Geeta, Akbar} be the set of students of XI class who are in School Hockey team. Let Y = {Geeta, David, Ashok} be the set of students of XI class who are in School Football team. Find `X uu Y` and `X nn Y` and interpret the set.

Let U be universal set of all students of class XI of a co-educational school and A be the set of all girls in class XI. Find A’.

Let A be the set of all students of class XII in a school and R be the relation, having the same sex on A, and then prove that R is an equivalence relation.

Let A be the set of all 50 students of class XII in a school. Let f: A rarr N be the function defined by : f (x) = Roll number of the student x. Prove that 'f' is one-one but not onto.

Let A be the set of the children in a family. The relation ‘x is a brother of y' relation on A is

If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n(X uu Y) = 38 , find n(X nn Y) .

Find the solution set of the system of linear contraints : x+yle6, xge1 and y<1 by graph.

For points P-=(x_1, y_1) and Q-=(x_2, y_2) of the coordinate plane, a new distance d(P ,Q)=|x_1-x_1|+|y_1-y_2| . Let O=(0,0) and A=(3,2) . Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.

Make correct statements by filling in the symbols sub or cancel sub in the blank spaces : {x : x is a student of Class XI of your school). . .{x : x student of your school)

Let N be the set of natural numbers and the relation R be defined on N such that R = {(x, y) : y = 2x, x, y in N} . Is this relation a function ?