Question

2. Given n (A)h = 285, n(B) = 195, n(U) = 500, n (A U B ) = 410, find n(A U B)

Answer 1

QUESTION :
Given n (A) = 285,n (B) = 195,n (U) = 500,n (A U B) = 410,find n (A' U 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 (A) = 285
n (B) = 195
n (U) = 500
n (A U B) = 410

n (A' U B') = n (A ∩ B)'

n (A ∩ B) = n (A) + n (B) - n (A U B)
n (A ∩ B) = 285 + 195 - 410
n (A ∩ B) = 480 - 410
n (A ∩ B) = 70

n (A ∩ B)' = n (U) - n (A ∩ B)
n (A ∩ B)' = 500 - 70
n (A ∩ B)' = 430

n (A' U B') = n (A ∩ B)'
n (A' U B') = 430

Hence, n (A' U B') = 430

HOPE THIS WILL HELP YOU...

Answer 2

Hi ,

It is given that ,

n( U ) = 500 ,

n( A ) = 285 ,

n( B ) = 195 ,

n( A U B ) = 410 ,

n( A' U B' ) = ?

******"******************************************

We know that ,

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

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

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

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

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

= 285 + 195 - 410

= 70

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

= 500 - 70

= 430

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

= 430

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

= 500 - 285

= 215

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

= 215

I hope this helps you.

: )