Question

2) If n(E) = 100, n(A) = 60, n(B) = 45, and n(AUB) = 85, find :
(i) n(ANB) (ii) n((AUB)') (iii) n(A-B).​

Answer 1

Answer:

Step-by-step explanation:

Given that,

n ( ξ ) = 100, n ( A ) = 60, n ( B ) = 45 and n ( A ∪ B ) = 85

1) n ( A ∩ B ) = n ( A) + n ( B ) - n ( A∪ B )

= 60 + 45 - 85

= 105 - 85

= 20

2) n ( A ∪ B ) = n ( A ) + n ( B ) - n ( A ∩ B )

= 60 + 45 - 20

= 105 - 20

= 85

∴ n ( ( A ∪ B ) ' ) = n ( ξ ) - n ( A ∪ B )

= 100 - 85

= 15

3) n ( A - B ) = n ( A ) - n ( A ∩ B )

= 60 - 20

= 40