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Sets Practice Test 1

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Question : 2 of 33

Marks: +1, -0

Two finite sets have x and y elements. Thenthe total number of subsets of the first set is56 more than the total number of subsets ofthe second. The value of x and y are:

7, 6
6, 3
5, 1
8, 7
None of the above

Solution: 👈: Video Solution

Concept:

A set with

n

elements has

2^n

subsets.

Explanation:

Let the first set have

x

elements and the second set have

y

elements.

Their subset counts are

2^x

and

2^y

.

Given:

2^x - 2^y = 56

Factor out

2^y

:

2^y(2^{x-y}-1)=56

Since

56=8 \times 7

and

2^{x-y}-1

is odd, compare powers of

2

.

Thus

2^y=8

, so

y=3

.

Then

2^{x-y}-1=7

, so

2^{x-y}=8

.

Hence

x-y=3

, giving

x=6

.

Check:

2^6-2^3=64-8=56

.

Answer:

The values are

x=6

and

y=3

, so the correct option is B.

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