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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)16
- b)15
- c)32
- d)31
Correct answer is option 'B'. Can you explain this answer?
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If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the ...
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
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If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} then find the ...
The set A has 8 elements, so the number of proper subsets can be found by using the formula 2^n - 1, where n is the number of elements in the set. Therefore, the number of proper subsets of A is 2^8 - 1 = 256 - 1 = 255.
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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)16b)15c)32d)31Correct answer is option 'B'. Can you explain this answer?
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