Question

Let a and b be two finites sets such that n(a) = m and n(b) = n. if the ratio of number of elements of power sets of a and b is 64 and n(a) + n(b) = 32. find the value of m and n.

Answer 1

number of elements in power set of set which order is n = 2^n
so according to que. 2^m/2^n= 64
2^(m-n) = 2^6
m-n =6. (1)
acc. to que.
m+n = 32 (2)
soo by 1 and 2 we get m=19 and n=13 ans.

Answer 2

Answer:

The values are m = 19 and n = 13

Step-by-step explanation:

If m is the number of elements in set a then the number of elements in the power set of a is given by $2^{m}$

If n is the number of elements in set b then the number of elements in the power set of b is given by $2^{n}$

The ratio of the number of elements in power sets of a and b is 64 therefore

$\frac{2^{m} }{2^{n} } =64$

$2^{m-n}=64$

$2^{m-n} =2^{6}$

m - n = 6

Given that

m + n = 32

add the above two equations

2m = 38

m = 19

n = 32 - 19

n = 13

Therefore m =19 and n = 13