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(A ∩ B)' is equal to
- a)(A' ∪ B)'
- b)A' ∪ B'
- c)A' ∩ B',
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
(A ∩ B)' is equal toa)(A' ∪ B)'b)A' ∪...
The intersection of two sets A and B, denoted by A ∩ B, is the set of all objects that are members of both the sets A and B. In symbols,
That is, x is an element of the intersection A ∩ B if and only if x is both an element of A and an element of B.
For example:
The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of odd numbers {1, 3, 5, 7, 9, 11, ...}, because 9 is not prime.
Intersection is an associative operation; that is, for any sets A, B, and C, one has A ∩ (B ∩ C) = (A ∩ B) ∩ C. Intersection is also commutative; for any A and B, one has A ∩ B = B ∩ A. It thus makes sense to talk about intersections of multiple sets. The intersection of A, B, C, and D, for example, is unambiguously written A ∩ B ∩ C ∩ D.
Inside a universe U one may define the complement A^c of A to be the set of all elements of U not in A. Now the intersection of A and B may be written as the complement of the union of their complements, derived easily from De Morgan's laws:
A ∩ B = (A^c ∪ B^c)^c
Most Upvoted Answer
(A ∩ B)' is equal toa)(A' ∪ B)'b)A' ∪...
Explanation:
The given expression is (A B). We need to determine its equivalent expression among the given options.
To understand the expression, let's break it down:
- (A B) represents the intersection of sets A and B. It includes all the elements that are common to both sets A and B.
Now, let's consider each option:
a) (A B)
- This option is the same as the given expression. It represents the intersection of sets A and B.
b) A B
- This option represents the union of sets A and B. It includes all the elements that are present in either set A or set B, or both.
c) A B
- This option represents the symmetric difference of sets A and B. It includes all the elements that are present in either set A or set B, but not in both.
d) None of these
- This option implies that none of the given options is the correct equivalent expression for (A B).
Correct answer: b) A B
The correct equivalent expression for (A B) is A B, which represents the union of sets A and B. This is because the given expression (A B) represents the intersection of sets A and B, not their union.
The given expression is (A B). We need to determine its equivalent expression among the given options.
To understand the expression, let's break it down:
- (A B) represents the intersection of sets A and B. It includes all the elements that are common to both sets A and B.
Now, let's consider each option:
a) (A B)
- This option is the same as the given expression. It represents the intersection of sets A and B.
b) A B
- This option represents the union of sets A and B. It includes all the elements that are present in either set A or set B, or both.
c) A B
- This option represents the symmetric difference of sets A and B. It includes all the elements that are present in either set A or set B, but not in both.
d) None of these
- This option implies that none of the given options is the correct equivalent expression for (A B).
Correct answer: b) A B
The correct equivalent expression for (A B) is A B, which represents the union of sets A and B. This is because the given expression (A B) represents the intersection of sets A and B, not their union.
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(A ∩ B)' is equal toa)(A' ∪ B)'b)A' ∪ B'c)A' ∩ B',d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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