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2 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.

a. 3 and 7

b. 7 and 3

c. 4 and 6

d.6 and 4

If the number of elements in a set is n, then the number of power sets of that setwill be =2nThus number power sets of A=2xThus number power sets of B=2ynow, according to given condition: 2x-2y=120                                                              2y( 2x-y-1)=120                                                                 2y( 2x-y-1)=8x15⇒ 2y=8 or y=3⇒and  2x-y-1=15 ⇒2x-y=16⇒x-y=4 ⇒x=4+y=4+3=7 
Ans. Option (b) satisfies this condition.

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The greater the power set of any set is , the greater the number of its elements will be .

So , n ( A ) = x ; P ( A ) = 2x and similarly , P ( B ) = 2y so ,P( A )-P( B ) = 120 Hence , x y

=2x- 2y = 120

= 2y{2 (x - y ) -1}= 120

= factorising 120 gives 23 * 3 * 5 and then equating the powers of 2 , 3 and 5

we get , y = 3 and2(x - y )-1 = 15

=2(x - y ) = 16

= x - y = 4 or x = 7

Thus , the values of x and y are 3 and 7 and the correct choice is a )3 and 7

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