JEE Exam > JEE Questions > Let A and B be two sets containing 4 and 2 el...
Start Learning for Free
Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, is
- a)256
- b)275
- c)219
- d)510
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Let A and B be two sets containing 4 and 2 elements, respectively. The...
To solve this problem, we need to find the number of subsets of the set AxB that have at least 3 elements.
First, let's find the total number of elements in the set AxB. Since A has 4 elements and B has 2 elements, the set AxB will have a total of 4 x 2 = 8 elements.
Now, let's consider the subsets of AxB.
- The number of subsets of a set with n elements is given by 2^n. Therefore, the total number of subsets of AxB is 2^8 = 256.
- However, we need to find the number of subsets that have at least 3 elements.
To find this, we can subtract the subsets with 0, 1, and 2 elements from the total number of subsets.
- The number of subsets with 0 elements is 1, as there is only one empty set.
- The number of subsets with 1 element can be found by selecting one element from the 8 elements of AxB. This can be done in 8C1 = 8 ways.
- The number of subsets with 2 elements can be found by selecting two elements from the 8 elements of AxB. This can be done in 8C2 = 28 ways.
Therefore, the number of subsets with at least 3 elements is 256 - 1 - 8 - 28 = 219.
Hence, the correct answer is option C) 219.
First, let's find the total number of elements in the set AxB. Since A has 4 elements and B has 2 elements, the set AxB will have a total of 4 x 2 = 8 elements.
Now, let's consider the subsets of AxB.
- The number of subsets of a set with n elements is given by 2^n. Therefore, the total number of subsets of AxB is 2^8 = 256.
- However, we need to find the number of subsets that have at least 3 elements.
To find this, we can subtract the subsets with 0, 1, and 2 elements from the total number of subsets.
- The number of subsets with 0 elements is 1, as there is only one empty set.
- The number of subsets with 1 element can be found by selecting one element from the 8 elements of AxB. This can be done in 8C1 = 8 ways.
- The number of subsets with 2 elements can be found by selecting two elements from the 8 elements of AxB. This can be done in 8C2 = 28 ways.
Therefore, the number of subsets with at least 3 elements is 256 - 1 - 8 - 28 = 219.
Hence, the correct answer is option C) 219.
Community Answer
Let A and B be two sets containing 4 and 2 elements, respectively. The...
n(A) = 4 and n(B) = 2
Therefore, n(A x B) = 8
Number of subsets of A x B having atleast 3 elements = 28 – 8C0 – 8C1 – 8C2
= 256 – 1 – 8 – 28
= 219
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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer?
Question Description
Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer?.
Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer?.
Solutions for Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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 A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let A and B be two sets containing 4 and 2 elements, respectively. Then the number of subsets of the set AxB, each having at least 3 elements, isa)256b)275c)219d)510Correct answer is option 'C'. 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