Two finite sets have m and n elements. The total number of subsets of the first set is 48 more than the total number of subsets of the second set. The value of m - n is

Explanation

Given, `8x -= 6` (mod 14)
`therefore lambda=(8x-6)/(14)`, where `lambdainI_(+)`
`therefore 8x=14lambda+6`
`implies x=(14lambda+6)/(8)`
`implies x=(7lambda+3)/(4)`
`=(4lambda+3(lambda+1))/(4)`
`x=lambda+(3)/(4)(lambda+1)`,where `lambdainI_(+)`
and here greatest common divisor of 8 and 14 is 2, so there are two required solutions.
For `lambda = 3` and 7, x = 6 and 13.