Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find `X ∪ Y` and interpret the set.

Let U be universal set of all the students of Class XI of a coeducational school and A be the set of all girls in Class XI. Find A′.

Let A be the set of all 50 students of Class X in a school Let f: A to N be function defined by f(x) = roll number of the student x. Show that f in one-one but not onto.

Let A be the set of all students of a boys school. Show that the relation R in A given by R = {(a,b):a is sister of b} is the empty relation and R' ={(a,b): the difference between heights of a and b is less than 3 meters } is the universal relation.

Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denotes the set of students and B denote the set of the sections. Define a relation from A to B as "x related to y if the student x belongs to the section y". Is this relation a function ? What can you say about the inverse relation ? Explain your answer.

Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. Let Y denote the number of students on that bus. Then E[X] and E[Y] respectively are

There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on separate cards, the cards being identical. Then she puts cards in a box and stirs them thoroughly. She then draws one card from the box. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

10 students of class-X took part in a mathematics quiz. If the number of girls is 4 more than the number of noys then, find the number of boys and the number of girls who took part in the quiz.

In Class XI of a school 40 % of the students study Mathematies and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathemetics or Biology.