Will u please tell me the exponential steps in the following ques
 
Two finite sets have m and n elements. The total no. Of subsets of the first set is 56 more than the total no. Of sunsets of the second set. Find the value of m and n.

Asked by takshu.kaushik | 26th Aug, 2016, 04:10: PM

Expert Answer:

begin mathsize 14px style Let space straight A space and space straight B space be space two space steps space having space straight m space and space straight n space elements space respectively.
Then space number space of space subsets space of space straight A space are space 2 to the power of straight m space and space number space of space subsets space of space straight B space are space 2 to the power of straight n.

Given space that comma space the space total space no. space of space subsets space of space the space first space set space is space 56 space more space than space the space total space no. space of space sunsets space of space the space second space set.
therefore 2 to the power of straight m minus 2 to the power of straight n space equals space 56
2 to the power of straight m cross times 2 to the power of straight n over 2 to the power of straight n minus 2 to the power of straight n space equals space 56 plus 8 minus 8
2 to the power of straight n open square brackets 2 to the power of straight m over 2 to the power of straight n close square brackets minus 2 to the power of straight n equals 64 minus 8
2 to the power of straight n open square brackets 2 to the power of straight m over 2 to the power of straight n minus 1 close square brackets equals 2 to the power of 6 minus 2 cubed................ open square brackets because straight a to the power of straight x over straight a to the power of straight y equals straight a to the power of straight x minus straight y end exponent close square brackets
2 to the power of straight n open square brackets 2 to the power of straight m cross times 2 to the power of negative straight n end exponent minus 1 close square brackets equals 2 cubed cross times 2 cubed minus 2 cubed............... open square brackets because straight a to the power of straight x straight a to the power of straight y equals straight a to the power of straight x plus straight y end exponent close square brackets
2 to the power of straight n open square brackets 2 to the power of straight m minus straight n end exponent minus 1 close square brackets equals 2 cubed open parentheses 2 cubed minus 1 close parentheses

Equating space the space exponentials space on space both space the space sides space we space get comma
straight n space equals space 3 space and space straight m minus straight n space equals space 3............. open square brackets because straight a to the power of straight x space equals space straight a to the power of straight y rightwards double arrow straight x space equals space straight y close square brackets
rightwards double arrow straight n space equals 3 space and space straight m space equals space 6 end style

Answered by Vijaykumar Wani | 26th Aug, 2016, 04:53: PM