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Let A and B be two sets containing four and two elements respectively.Then the number of subsets of the set A×B,each having atleast three elements is:
- a)219
- b)256
- c)275
- d)510
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let A and B be two sets containing four and two elements respectively....
⇒ Number of elements in Set A = 4
⇒ Number of elements in Set B = 2
∴ Number of elements in set (A × B) = 8
∴ Total number of subsets of (A×B) = 28 = 256
⇒ Number of subsets having 0 elements = 8C0 = 1
⇒ Number of subsets having 1 element = 8C1 = 8
⇒ Number of subsets having 2 elements = 8C2 = 28
∴ Number of subsets having atleast 3 elements = 256 - 1 - 8 - 28 = 219
⇒ Number of elements in Set B = 2
∴ Number of elements in set (A × B) = 8
∴ Total number of subsets of (A×B) = 28 = 256
⇒ Number of subsets having 0 elements = 8C0 = 1
⇒ Number of subsets having 1 element = 8C1 = 8
⇒ Number of subsets having 2 elements = 8C2 = 28
∴ Number of subsets having atleast 3 elements = 256 - 1 - 8 - 28 = 219
Most Upvoted Answer
Let A and B be two sets containing four and two elements respectively....
The number of subsets of a set with n elements is 2^n. Therefore, the number of subsets of set A, which contains 4 elements, is 2^4 = 16.
Community Answer
Let A and B be two sets containing four and two elements respectively....
Elements in A*B IS 8
SO ans.is 2^8-8c1-8c2-8c0
256-8-28-1=219
SO ans.is 2^8-8c1-8c2-8c0
256-8-28-1=219
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Let A and B be two sets containing four and two elements respectively.Then the number of subsets of the set A×B,each having atleast three elements is:a)219b)256c)275d)510Correct answer is option 'A'. Can you explain this answer?
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