Condition for monoid is __________a)(a+e)=ab)(a*e)=(a+e)c)a= a*(a+e)d)(a*e)=(e*a)=aCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

B
2^m = 56+2^n
2^m-2^n = 56
m=6
n=3

Answer

No. of subset containing m elements =2 ^m
no.of subset containing n elements =2^n
according to question , 2^m-2^n = 56
2 ^n ( 2^(m-n) - 1) =2^3 *(2^3 -1 )
therefore n= 3 and m = 6

Answer

Correct answer is b) 6,3

explanation - if m=6 then total number of subset is 2^6=64
and if n=3 then total number of subset is 2^3=8
then no. of subset of (m)=56+no.of subset of (n) i.e
64=56+8
from above we conclude that option (b) is correct

Answer

To solve this problem, let's assume that the first set has 'm' elements and the second set has 'n' elements. We need to find the values of 'm' and 'n'.

Let's calculate the total number of subsets for each set:

For the first set with 'm' elements:
The total number of subsets of a set with 'm' elements is given by 2^m.

For the second set with 'n' elements:
The total number of subsets of a set with 'n' elements is given by 2^n.

According to the problem, the total number of subsets of the first set is 56 more than the total number of subsets of the second set. Mathematically, this can be expressed as:

2^m = 2^n + 56

Now, let's solve this equation to find the values of 'm' and 'n'.

Taking the logarithm of both sides of the equation:

log(2^m) = log(2^n + 56)

Using the logarithmic property log(a^b) = b * log(a):

m * log(2) = n * log(2) + log(2^3 * 7)

Simplifying further:

m * log(2) - n * log(2) = log(8 * 7)

(log(2) is common for both terms on the left side)

m - n = log(56) / log(2)

Since 'm' and 'n' are the number of elements, they should be integers. The only option that satisfies this condition is option 'B' with 'm = 6' and 'n = 3'.

Therefore, the values of 'm' and 'n' are 6 and 3, respectively.

Top Courses for Mathematics

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams