Two finite sets A and B have x and y elements respectively. The number of elements in the power set of A is 120 more than the number of elements in the power set of B. What are the values of x and y respectively?

  • 3 and 7

  • 7 and 3

  • 4 and 6

  • 6 and 4

  • 0

If the original set has n elements, the power set has 2n elements.

Now

2x = Number of elements of P(A)

2y = Number of elements of P(B)

2x = 2y + 120

We now that 27 = 128 (closest to 120)

128 = 2y + 120

2y = 8

y = 3

Thus x = 7, y = 3

  • 0
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