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Let x = {n ∈ N : 1 ≤ n ≤ 50}. If A = {n ∈ X : n is a multiple of 2} and B = {n ∈ X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.
Correct answer is '29'. Can you explain this answer?
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Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multi...
Explanation:
Defining the Sets:
- Let X = {n ∈ N : 1 ≤ n ≤ 50} be the set of natural numbers from 1 to 50.
- A = {n ∈ X : n is a multiple of 2} is the set of even numbers in X.
- B = {n ∈ X : n is a multiple of 7} is the set of numbers in X that are multiples of 7.
Finding the Elements in A and B:
- To find the elements in A, we need to identify the even numbers in X, which are {2, 4, 6, ..., 50}. There are 25 even numbers in X.
- To find the elements in B, we need to identify the multiples of 7 in X, which are {7, 14, 21, 28, 35, 42, 49}. There are 7 multiples of 7 in X.
Finding the Intersection of A and B:
- The smallest subset of X containing both A and B will be the set of numbers that are both even and multiples of 7.
- The numbers that satisfy this condition are {14, 28, 42}, which are 3 in total.
Therefore, the number of elements in the smallest subset of X containing both A and B is 3.
Defining the Sets:
- Let X = {n ∈ N : 1 ≤ n ≤ 50} be the set of natural numbers from 1 to 50.
- A = {n ∈ X : n is a multiple of 2} is the set of even numbers in X.
- B = {n ∈ X : n is a multiple of 7} is the set of numbers in X that are multiples of 7.
Finding the Elements in A and B:
- To find the elements in A, we need to identify the even numbers in X, which are {2, 4, 6, ..., 50}. There are 25 even numbers in X.
- To find the elements in B, we need to identify the multiples of 7 in X, which are {7, 14, 21, 28, 35, 42, 49}. There are 7 multiples of 7 in X.
Finding the Intersection of A and B:
- The smallest subset of X containing both A and B will be the set of numbers that are both even and multiples of 7.
- The numbers that satisfy this condition are {14, 28, 42}, which are 3 in total.
Therefore, the number of elements in the smallest subset of X containing both A and B is 3.
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Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multi...
∵ X = {1, 2, 3, 4, ..., 50}
A = {2, 4, 6, 8, ..., 50}
B = {7, 14, 21, 28, 35, 42, 49}
Here, n(A ∪ B) = n(A) + n(B) - n(A ∪ B) = 25 + 7 - 3 = 29
∴ The number of elements in the smallest subset of X containing both A and B is 29.
A = {2, 4, 6, 8, ..., 50}
B = {7, 14, 21, 28, 35, 42, 49}
Here, n(A ∪ B) = n(A) + n(B) - n(A ∪ B) = 25 + 7 - 3 = 29
∴ The number of elements in the smallest subset of X containing both A and B is 29.
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Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer?
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Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer?.
Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let x = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.Correct answer is '29'. Can you explain this answer?.
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