Question

Let A and B be two sets such that n(A) = 45, n(B) = 30 and n(AUB) = 65. Find n(ANB) [Here, n(X) denotes the number of elements in set x]​

Answer 1

Step-by-step explanation:

Given :-

A and B be two sets such that n(A) = 45, n(B) = 30 and n(AUB) = 65.

To find :-

Find n(A∩B) ?

Solution :-

Given that :

n(A) = 45

n(B) = 30

n(AUB) = 65

We know that

Fundamental Theorem on Sets

n(AUB) = n(A)+n(B)-n(A∩B)

=> n(A∩B) = n(A)+n(B)-n(AUB)

On Substituting these values in the above formula then

=> n(A∩B) = 45 + 30 - 65

=> n(A∩B) = 75 - 65

=> n(A∩B) = 10

Therefore , n(A∩B) = 10

Answer:-

The value of n(A∩B) for the given problem is 10

Used formulae:-

Fundamental Theorem on Sets:-

If A and B are two sets then

n(AUB) = n(A)+n(B)-n(A∩B) .

Where,

n(A) = Number of elements in A

n(B) = Number of elements in B

n(AUB) = Number of elements in AUB

n(A∩B) = Number of elements in A∩B

AUB = {x:x€ A or x€B}

A∩B ={x:x€A and x€B}

Answer 2

Answer:

answer for the question