Question

Two finite sets have m and n elements. The total number of subsets of the first set is 112 more than the total number of subsets of the second set. Find the valuesof m and n.

Answer 1

Hey mate!!!

Number of subsets of the two sets = 2m and 2n, respectively (Formula)

According to the question,

2m = 2n – 112

ð   2m - 2n = 112

ð  2n (2m / 2n - 1) = 24 (7)

ð  2n ( 2m - n - 1) = 24 ( 7 )

2n cannot be equal to 7 (since 2n = 2 x 2 x 2 x 2 x .........)

Therefore, 2n = 24

Equating the powers of 2, we get:

n = 4.......... (1)

Also, 2m - n -1 = 7

ð  2m - n = 7+1 = 8

ð  2m - n = 23 (since 8 = 23)

Equating the powers of 2, we get:

m - n= 3

ð   m = n+3 = 4+3     ( From (1) )

ð   m = 7

HOPE IT HELPS.

Answer 2

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The answer of u r question is..✌️✌️

Ans:✍️✍️✍️✍️✍️✍️


Number of sets of two sets = 2m and 2n


$= 2m = 2n - 112$

$2 m- 2 n= 112$


$2n\frac{(2m - 1)}{2n} = 24(7)$


$2n(2m - n - 1) = 24(7)$


$2n = 24$



$n = 4$

$2m - n - 1 = 7$


$2m - n = 7 + 1 = 8$


$2m - n = 23$


$m - n = 3$


$m = n + 3 = 4 + 3 = 7$


$= 7$


Thank you..⭐️⭐️⭐️