JEE Exam > JEE Questions > Let x = {n ∈N : 1 ≤n ≤50}. If A = ...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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.
Free Test
FREE
| Start Free Test |
Community Answer
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.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup