Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4...
Start Learning for Free
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?
- a)15
- b)16
- c)32
- d)31
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the ...
A proper subset of A is any subset of A that is not equal to A itself.
To find the number of proper subsets of A, we first need to find the total number of subsets of A. We can do this by noting that each element of A can either be included or excluded from a subset, giving us 2 choices for each element. Therefore, the total number of subsets of A is 2^8 = 256.
However, this includes the subset containing all elements of A, which is not a proper subset. Therefore, we need to subtract 1 from 256 to get the number of proper subsets:
256 - 1 = 255
Therefore, there are 255 proper subsets of A.
To find the number of proper subsets of A, we first need to find the total number of subsets of A. We can do this by noting that each element of A can either be included or excluded from a subset, giving us 2 choices for each element. Therefore, the total number of subsets of A is 2^8 = 256.
However, this includes the subset containing all elements of A, which is not a proper subset. Therefore, we need to subtract 1 from 256 to get the number of proper subsets:
256 - 1 = 255
Therefore, there are 255 proper subsets of A.
Free Test
FREE
| Start Free Test |
Community Answer
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the ...
CONCEPT:
Intersection:
Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.
The intersection of A and B is denoted by A ∩ B i.e A ∩ B = {x : x ∈ A and x ∈ B}
Note: If A is a non-empty set such that n(A) = m then numbers of proper subsets of A is given by 2m - 1.
Intersection:
Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.
The intersection of A and B is denoted by A ∩ B i.e A ∩ B = {x : x ∈ A and x ∈ B}
Note: If A is a non-empty set such that n(A) = m then numbers of proper subsets of A is given by 2m - 1.
CALCULATION:
Given: A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9}
As we know that, A ∩ B = {x : x ∈ A and x ∈ B}
⇒ A ∩ B = {2, 4, 7, 9}
As we can see that,
The number of elements present in A ∩ B = 4
i.e n(A ∩ B) = 4
As we know that;
If A is a non-empty set such that n(A) = m then
The numbers of proper subsets of A are given by 2m - 1.
So, The number of proper subsets of A ∩ B = 24 - 1 = 15
Hence, the correct option is 2
Given: A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9}
As we know that, A ∩ B = {x : x ∈ A and x ∈ B}
⇒ A ∩ B = {2, 4, 7, 9}
As we can see that,
The number of elements present in A ∩ B = 4
i.e n(A ∩ B) = 4
As we know that;
If A is a non-empty set such that n(A) = m then
The numbers of proper subsets of A are given by 2m - 1.
So, The number of proper subsets of A ∩ B = 24 - 1 = 15
Hence, the correct option is 2
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer?
Question Description
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer?.
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer?.
Solutions for If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the number of proper subsets of A ∩ B ?a)15b)16c)32d)31Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
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