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Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are:    
  • a)
    7,6
  • b)
    6,3
  • c)
    5,1
  • d)
    8,7
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Two finite sets have m and n elements. The total number of subsets of ...
To solve this problem, let's first consider the formula for the number of subsets of a set.

The number of subsets of a set with 'n' elements is 2^n.

Let's assume the first set has 'm' elements and the second set has 'n' elements.

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.

So, we can write the equation:

2^m = 2^n + 56

To solve this equation, we need to find values of 'm' and 'n' that satisfy this equation.

Let's analyze the given options one by one:

Option A: m = 7, n = 6

Substituting the values in the equation:

2^7 = 2^6 + 56

128 = 64 + 56

128 ≠ 120

So, option A is not the correct answer.

Option B: m = 6, n = 3

Substituting the values in the equation:

2^6 = 2^3 + 56

64 = 8 + 56

64 = 64

The equation is satisfied.

So, option B is the correct answer.

Option C: m = 5, n = 1

Substituting the values in the equation:

2^5 = 2^1 + 56

32 = 2 + 56

32 ≠ 58

So, option C is not the correct answer.

Option D: m = 8, n = 7

Substituting the values in the equation:

2^8 = 2^7 + 56

256 = 128 + 56

256 ≠ 184

So, option D is not the correct answer.

Therefore, the correct answer is option B: m = 6, n = 3.
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Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are:a)7,6b)6,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer?
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