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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?
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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.
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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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? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 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? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
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