Question

1. If A and B are two sets and U is the universal set such that n (U)= 700,n(A)= 200, n(B) = 300 and n(A u B) = 100, find n(A U B).

Answer 1

QUESTION:
If A and B are two sets and U is the universal set such that n (U) = 700, n (A) = 200, n(B) = 300 and n (A ∩ B) = 100,find n (A' ∩ B').


CARDINAL NUMBER OF A FINITE SET :
The Cardinal number of a finite set A is the number of distinct elements in the set A. It is denoted by n(A).
•It is not possible to define the Cardinal number of an infinite set.
•The Cardinal number of the empty set is zero.
•The Cardinal number of a singleton set is 1.

SOLUTION:

GIVEN ;
n (U) = 700
n (A) = 200
n(B) = 300
n (A ∩ B) = 100

n (A' ∩ B') = n (A U B)'

n (A U B) = n (A) + n (B ) - n (A ∩ B)
n (A U B) = 200 + 300 - 100
n (A U B) = 500 - 100
n (A U B) = 400

n (A U B)' = n (U) - n (A U B)
n (A U B)' = 700 - 400
n (A U B)' = 300

n (A' ∩ B') = n (A U B)'

n (A' ∩ B') = 300

Hence, n (A' ∩ B') = 300

HOPE THIS WILL HELP YOU...

Answer 2

Hi ,

It is given that ,

A and B are two sets .

U is the Universal Set .

n( U ) = 700 ,

n( A ) = 200

n( B ) = 300 ,

n ( A n B ) = 100 ,

n( A' U B' ) = ?

***************************************************

We know that ,

1 ) n( A U B ) = n( A ) + n( B ) - n( A n B )

2 ) n ( A U B )' = n( U ) - n( A U B )

3 ) n ( A' n B' ) = n( A U B )'

**************************************************

1 ) n( A U B ) = n( A ) + n( B ) - n( A n B )

= 200 + 300 - 100

= 400 -------- ( i )

2 ) n( A U B )' = n( U ) - n( A U B )

= 700 - 400

= 300 ------( ii )

3 ) n( A' U B' ) = n( U ) - n( A n B )

= 700 - 100

= 600 ----( iii )

4 ) n( A' n B' ) = n( A U B )'


= 300 ---[ from ( ii ) ]


I hope this helps you.

: )