Question

if A and B are two finite sets such that total number of subsets of a is 960 more than the total number of subsets of B then and Bracket a minus and Bracket B where and X denote the number of element in a set x is equal to

Answer 1

Answer:

4

Step-by-step explanation:

Given If A and B are two finite sets such that total number of subsets of a is 960 more than the total number of subsets of B then and Bracket a minus and Bracket B where and X denote the number of element in a set x is equal to

Let the total number of elements in set A be x

 So the subsets of set A will be 2 ^x

Again let total number of elements in set B be y

So subsets of set B will be y

Given in the problem

 Subset of A = 960 + total subsets of B

  2 ^x = 960 + 2 ^y

  2 ^x - 2 ^y = 960

 taking 2 ^y as common we get

 2 ^y {2 ^ (x - y) - 1} = 15 x 2^6 [ factors of 960]

  2 ^ y = 2 ^ 6

   y = 6 (when bases are same exponents are equal)

Similarly 2 ^(x - y) - 1 = 15

          2 ^ (x - y) = 16

         2 ^ (x - y) = 2 ^ 4

        x - y = 4

       x - 6  = 4

       x = 10

So n (A) - n(B) = x - y = 10 - 6 = 4

option 4 is the right answer.

Answer 2

Answer:

4

Step-by-step explanation:

concept:

If A contains m elementas then n[P(A)] contains 2^m elements.

Let x and y be the number of elements of A and B respectively.

That is

n(A)= x, n(B)= y

As per given data,

n[P(A)] = n[P(B)]+960

n[P(A)] - n[P(B)]=960

$2^x-2^y=960 \\ \\ 2^x-2^y=1024-64 \\ \\ 2^x-2^y=2^{10}-2^6$

comparing on both sides we get

x=10 and y=6

x - y = 10 - 6 = 4