Question

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are

• A. 7, 6
• B. 6, 3
• C. 5, 1
• D. 8, 7

Answer 1

Answer: (B)

6, 3

Answer 2

Since $2 ^ { m } - 2 ^ { n } = 56 = 8 \times 7 = 2 ^ { 3 } \times 7$

⇒ $2 ^ { n } \left( 2 ^ { m - n } - 1 \right) = 2 ^ { 3 } \times 7$

$\therefore$ $2 ^ { m - n } = 8 = 2 ^ { 3 }$

⇒ $m - 3 = 3$ ⇒ $m = 6$

$\therefore m = 6 , n = 3$.