Question

If n(∪) =50, n(A) =3x, n(B) =2x And n(A∩B) = x = n((A∪B)’), Find n(A - B)

Answer 1

Answer:

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Answer 2

Answer:

n(A-B) = 20

Step-by-step explanation:

Step 1 -

Given,

n(U) = 50

n(A) = 3x

n(B) = 2x

n(A∩B) = n((AUB)') = x

also,

n(AUB) = n(A)+n(B) -n(A∩B)

$n(AUB) = 3x+ 2x-x = 4x$

Step 2 -

n((AUB)') = 50 - 4x

but given n((AUB)') = x

So,

$50-4x = x\\\\5x = 50\\\\x = 10$

We got x = 10

Step 3 -

n(A-B) = n(A) - n(A∩B)

$n(A-B) = 3x-x =2x =2\times 10 =20$

We got n(A - B) = 20

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