Question

Let A and B be two sets such that n (A) = 24, nat
N(AUB) = 46 and n(AinteractioB) = 8 Find
i) n(B) ii) n(A-B) iii) n(b-A) ​

Answer 1

SOLUTION

GIVEN

Let A and B be two sets such that n (A) = 24 , n(A∪B) = 46 and n(A ∩ B) = 8

TO DETERMINE

i) n(B)

ii) n(A - B)

iii) n(B - A)

EVALUATION

Here it is given that A and B be two sets such that

n (A) = 24 , n(A ∪ B) = 46 and n(A ∩ B) = 8

Now

i) n(A ∪ B) = 46

⇒ n(A) + n(B) - n(A ∩ B) = 46

⇒ 24 + n(B) - 8 = 46

⇒ 16 + n(B) = 46

⇒ n(B) = 46 - 16

⇒n(B) = 30

∴ n(B) = 30

ii) n(A - B)

= n(A) - n(A ∩ B)

= 24 - 8

= 16

∴ n(A - B) = 16

iii) n(B - A)

= n(B) - n(B ∩ A)

= n(B) - n(A ∩ B)

= 30 - 8

= 22

∴ n(B - A) = 22

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U).

https://brainly.in/question/4193770

2. If A, B and C are any three sets then prove the following using venn-diagram

A∩(BUC) = (A∩B) U (A∩C)

https://brainly.in/question/23234089