Question

Let n (A)=50 n (A'uB') = 40
n(u)=60 then find n (A-B) ?

Answer 1

Step-by-step explanation:

let n(A) = 50 n(A' UB') = 40

n(U) = 60 then find n(A-B)?

Shot by Änji 2021 09 12 00:34

Answer 2

Answer:

The required answer is n(A - B) = 20.

Step-by-step explanation:

Given:-

n(A) = 50, n(A'∪B') = 40, n(U) = 60.

To find:-

n(A - B) =?

Step 1 of 1

It is given that n(A'∪B') = 40.

Using De Morgan's law of intersection, we have

n(A∩B)' = n(A'∪B')

n(A∩B)' = 40 ____ (1)

Also,

n(A∩B) = n(U) - n(A∩B)'

            = 60 - 40 (From (1))

            = 20

As we know,

n(A∪B) = n(A) + n(B) - n(A∩B)

Substitute the values of n(A) and n(A∩B) as follows:

⇒ n(A∪B) = 50 + n(B) - 20

⇒ n(A∪B) = 30 + n(B)

⇒ n(A∪B) - n(B) = 30

⇒ n(A - B) = 20 (Since n(A∪B) - n(B) = n(A - B))

Final answer: The required answer is n(A - B) = 20.

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