Question

5) Two finite sets A and B have m and k elements respectively. If the ratio of
total no. of subsets of A to total number of subsets of B is 64:1 and
n(A) + n(B)=12. Then find the values of m and k.​

Answer 1

Step-by-step explanation:

which is required ans.

Answer 2

The value of m = 9 and k = 3

Given:

m and k are two finite sets

Ratio of total number of subsets = 64 : 1

n(A) + n(B) = 12

To Find:

The value of m and k.

Step-by-step explanation:

n(A) = m and n(B) = k (given)

Total number of subsets in A = $2^{m}$

Total number of subsets in A = $2^{k}$

$\frac{2^{m}}{2^{k}}$ = $\frac{64}{1}$

$2^{m-k}$ = $2^{6}$

m - k = 6                                                                        (1)

n(A) + n(B) = 12

On comparing n(A) + n(B) = 12 with m - k = 6      

we get m + k = 12                                                          (2)

Equation (1) + (2)

we get 2m = 18

              m = 9

Equation (2) - (1)

we get 2k = 6

             k = 3