32. If A and B are two sets such that n(only A) = 14 + x, n( only B) = 3x, n(ANB) = x. Draw a Venn
diagram to illustrate this.
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Step-by-step explanation:
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n(a-b)=20+x
n(b-a)=3x
n(a ∩ b) =x+1
We know that
n(a-b) = n(a)-n(a ∩ b)
∴n(a) = n(a-b) + n(a ∩ b)
= (20+x) + (x + 1)
= 2x + 21
Similarly, n(b) = n(b-a) + n(a ∩ b)
=3x + (x+1)
=4x + 1
According to the question,
n(a) = n(b)
∴2x + 21 = 4x +1
⇒2x = 20
∴ x = 10
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