Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:

Question

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are: (A)  7,6  (B)  6,3  (C)  6,4  (D)  7,4

Tardigrade Admin · Accepted Answer

According to the given condition 2m-2n=48 This is possible only when m=6 and n=4 .

Q. Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in the power set of the second set. Then the values of m and n are:

$7, 6$

$6, 3$

$6, 4$

$7, 4$

$3, 7$

According to the given condition $2^{m} - 2^{n} = 48$ This is possible only when $m = 6$ and $n = 4$ .