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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?
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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
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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?
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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?.
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