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Two Unite 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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Two Unite sets have m and n elements. The total number of subsets of t...
Given Information:
- Two 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
Solution:
Number of Subsets of a Set:
- The number of subsets of a set with 'n' elements is given by 2^n
- Therefore, the number of subsets of the first set with 'm' elements is 2^m
- The number of subsets of the second set with 'n' elements is 2^n
Given Condition:
- The total number of subsets of the first set is 56 more than the total number of subsets of the second set
- This can be mathematically represented as: 2^m = 2^n + 56
Substitute the Values:
- We know that m = n + 3 (as per the options)
- Substitute m = n + 3 in the given condition: 2^(n+3) = 2^n + 56
- Simplify the equation: 2^n * 2^3 = 2^n + 56
- Further simplify: 8 * 2^n = 2^n + 56
- Rearrange: 7 * 2^n = 56
- Solve for n: 2^n = 8, n = 3
Therefore, the correct values for m and n are 6 and 3 respectively, which matches with option B.
- Two 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
Solution:
Number of Subsets of a Set:
- The number of subsets of a set with 'n' elements is given by 2^n
- Therefore, the number of subsets of the first set with 'm' elements is 2^m
- The number of subsets of the second set with 'n' elements is 2^n
Given Condition:
- The total number of subsets of the first set is 56 more than the total number of subsets of the second set
- This can be mathematically represented as: 2^m = 2^n + 56
Substitute the Values:
- We know that m = n + 3 (as per the options)
- Substitute m = n + 3 in the given condition: 2^(n+3) = 2^n + 56
- Simplify the equation: 2^n * 2^3 = 2^n + 56
- Further simplify: 8 * 2^n = 2^n + 56
- Rearrange: 7 * 2^n = 56
- Solve for n: 2^n = 8, n = 3
Therefore, the correct values for m and n are 6 and 3 respectively, which matches with option B.
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Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer?
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Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer?.
Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer?.
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Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two Unite 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 area)7,6b)6 ,3c)5,1d)8,7Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two Unite 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 area)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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