SEE MATH Classes

Examples1

In a group of 200 students who like game, 120 like cricket game an 105 like football game. By drawing Venn diagram find

i. how many students like both the games ?
ii. How many students like only cricket?

Soln

n(U) = 200
C and F denote the students who study Cricket and football respectively.

n(C) =120

n(F) = 105

n( C ∩ F)=?

We have

n(CUF)=n(C) + n(F) -n(C∩ F)

200=120 + 105 -n(C∩ F)

n(C∩ F)= 25

n0(C) = n(C)-n( C ∩ F)= 120 – 25 = 95

SETS

Sets-: In mathematics set is defined as the collection of well defined object which can be separated distinctly.

For instance,
S = {2, 4, 6, 8} is collection of the even integers.

A set can be explained in different ways:

i. Listing method: A = {a, b, c, .z}

ii. Descriptive method: N = {the natural numbersfrom 1 to 50}

iii. Set builder method: A – B= A -(A∩ B )

iv. Venn – diagram

Universal sets-:A universal set is the collection of all objects in a particular context or theory. All other sets in that framework constitute subsets of the universal set, which is denoted as letter U. The objects themselves are known as elements or members of U.

Subsets-:The set made by elements of the universal sets is called subsets of the universal sets

For example

U = {1, 2, 3, 4, …………..50}
A = {even integers from 1 to 50}
B= {odd numbers from 1 to 50}

Here, A and B are the subsets of U