Question

One of a group of 60 students,25 play cricket,24 Play volleyball,10play cricket and football,9 cricket and volleyball,12 Play volleyball and football and 5 Play all the three.
How many students play exactly two games​

Answer 1

Correct Question

In a class of 60 student, 25 students play cricket and 20 students play tennis, and 10 students play both the games, then the number of students who play neither are

Given

• There are total 60 students in the class.
• 25 students play cricket.
• 20 students play tennis.
• 10 students play both the games.

Required to Find

Number of students who neither play

Solution

Let A be the set of students who play cricket.

B be the set of students who play tennis.

It is given that, n( A ) = 25 , n( B ) = 20 and n( A ∩ B ) = 10 = students who play both the games

Thus,

n(. A U B ) = n( A ) + n( B ) - n( A ∩ B ) = 20 + 25 - 10 = 35

Therefore the students who played neither of the cricket and tennis = 60 - 35 = 25.

More

Union set

The union of a set A with B is the set of elements that are in either set A or B. The union is denoted as A U B.

A union is an organized group of workers who come together to make a decision about the condition of their work.

Properties of set

• Set can have elements.
• and that two sets are equal (one and the same ) if and only if every element of each set is an element of the other.

Types of set

Finite set

If a set is a null set or number if elements are limited and countable then it is called as finite set.

Infinite set

If the number of elements in a set is unlimited and uncountable then the set is called as Infinite set

Subset

if A and B are two given sets and every element of Set B is also an element of set a then B is a subset of A.

Universal set

think of a bigger set which will accommodate all the given sets under consideration which in general is known as universal set .so that the sets under consideration are the subsets of the universal set

Empty set it Null set

If there is not a single element in the set which satisfies the given condition then it is called Nulls set or an empty set.

Singleton set

A set consisting of a single element is called a singleton set.

Equal set

Two set A and B are said to be equal, if every element of set A is in set B and every element of Set B is in set A.

' Set A and set B are equal set ', symbolically it is written as A = Ba