A and B are two overlapping sets such that n(A ∩ B) = x + 4, n(A - B) = 4x - 8 and n(B) = 3x + 8. Find x, if n(A ∪ B) = 70. Also, find n(A' ∩ B).
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NOTE*: I'll use (int.) for intersection since I dont know the maths formatting used . Comment if you know .
Answer :
n(A U B) = n(A)+n(B) - n(A int. B)
=> 70 = n(A)+3x+8 - x - 4 = n(A)+2x+4
=> n(A) = 70 - 2x-4 = 66-2x
n(A-B)=n(A)-n(A int. B)
=> 4x-8 = 66-2x-x-4 = 62-3x
=> 7x = 70
=> x = 10
n(A' int. B) = n(B-A) = n(B) - n(A int. B)
= 3x+8 - x - 4 = 2x + 4
since x = 10
Therefore n(A' int. B) = 2x + 4 = 20 + 4 = 24
Answer :
n(A U B) = n(A)+n(B) - n(A int. B)
=> 70 = n(A)+3x+8 - x - 4 = n(A)+2x+4
=> n(A) = 70 - 2x-4 = 66-2x
n(A-B)=n(A)-n(A int. B)
=> 4x-8 = 66-2x-x-4 = 62-3x
=> 7x = 70
=> x = 10
n(A' int. B) = n(B-A) = n(B) - n(A int. B)
= 3x+8 - x - 4 = 2x + 4
since x = 10
Therefore n(A' int. B) = 2x + 4 = 20 + 4 = 24
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