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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?
- a)12
- b)21
- c)27
- d)30
Correct answer is option 'D'. Can you explain this answer?
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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset...
To solve this problem, let's break it down into smaller steps:
1. Finding the set A:
The set A is defined as {x | x > 9, x is a natural number}.
This means that the set A consists of all natural numbers greater than 9.
2. Finding the subset B:
The subset B is defined as {a, b, c} where (a + b + c) is a multiple of 3.
In other words, the sum of any three elements in subset B must be divisible by 3.
3. Determining the largest possible number of subsets like B:
To find the largest possible number of subsets like B, we need to consider the elements of set A that satisfy the condition of subset B.
Let's analyze the possible values for a, b, and c:
- If a = 10, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 12, c = 15).
- If a = 11, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 12, c = 18).
- If a = 12, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 18).
- If a = 13, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 21).
- If a = 14, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 24).
- If a = 15, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 18, c = 21).
From the above analysis, we can see that for each value of a from 10 to 15, there are 4 possible combinations for b and c. Therefore, the number of subsets like B is 6 (values for a) * 4 (combinations for b and c) = 24.
However, we need to consider one more case:
- If a = 16, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 18, c = 24).
So, when a = 16, there is an additional possibility, making the total number of subsets like B to be 25.
Therefore, the correct answer is option 'D' (30), which is the largest possible number of subsets like B.
1. Finding the set A:
The set A is defined as {x | x > 9, x is a natural number}.
This means that the set A consists of all natural numbers greater than 9.
2. Finding the subset B:
The subset B is defined as {a, b, c} where (a + b + c) is a multiple of 3.
In other words, the sum of any three elements in subset B must be divisible by 3.
3. Determining the largest possible number of subsets like B:
To find the largest possible number of subsets like B, we need to consider the elements of set A that satisfy the condition of subset B.
Let's analyze the possible values for a, b, and c:
- If a = 10, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 12, c = 15).
- If a = 11, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 12, c = 18).
- If a = 12, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 18).
- If a = 13, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 21).
- If a = 14, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 15, c = 24).
- If a = 15, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 18, c = 21).
From the above analysis, we can see that for each value of a from 10 to 15, there are 4 possible combinations for b and c. Therefore, the number of subsets like B is 6 (values for a) * 4 (combinations for b and c) = 24.
However, we need to consider one more case:
- If a = 16, then b and c can be any two elements from set A that are multiples of 3 (e.g., b = 18, c = 24).
So, when a = 16, there is an additional possibility, making the total number of subsets like B to be 25.
Therefore, the correct answer is option 'D' (30), which is the largest possible number of subsets like B.
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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset...
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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?a)12b)21c)27d)30Correct answer is option 'D'. Can you explain this answer?
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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?a)12b)21c)27d)30Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?a)12b)21c)27d)30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?a)12b)21c)27d)30Correct answer is option 'D'. Can you explain this answer?.
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