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If A and. B are two disjoint sets, then which one of the following is correct?
- a)A - B = A - (A ∩ B)
- b)B - A' = B ∩ A
- c)A ∩ B = (A-B) ∩ B
- d)All of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If A and. B are two disjoint sets, then which one of the following is ...
Since, A ∩ B = φ (given)
So, A - B = A - ( A ∩ B )
(Since, A - B = A)
Now, B - A' = φ
and B ∩ A = φ
or B ‘- A ' = B ∩ A
and (A- B ) ∩ B = A ∩ B
So, option (d) is correct.
So, A - B = A - ( A ∩ B )
(Since, A - B = A)
Now, B - A' = φ
and B ∩ A = φ
or B ‘- A ' = B ∩ A
and (A- B ) ∩ B = A ∩ B
So, option (d) is correct.
Most Upvoted Answer
If A and. B are two disjoint sets, then which one of the following is ...
Explanation:
Disjoint Sets:
Disjoint sets are sets that have no elements in common. In other words, the intersection of two disjoint sets is an empty set.
Option 'A':
A - B represents the set of elements that are in set A but not in set B. A ∩ B represents the set of elements that are common to both set A and set B. So, A - (A ∩ B) represents the elements that are in set A but not in the intersection of sets A and B. This is equivalent to A - B.
Option 'B':
B - A represents the set of elements that are in set B but not in set A. Aᶜ represents the complement of set A. So, B ∩ Aᶜ represents the set of elements that are in set B and not in set A. This is equivalent to B - A.
Option 'C':
A ∩ B represents the set of elements that are common to both set A and set B. (A-B) represents the set of elements that are in set A but not in set B. (A-B) ∩ B represents the set of elements that are in set A but not in set B, and also in set B. This is equivalent to A ∩ B.
Conclusion:
Since all the given options correctly represent the operations on disjoint sets A and B, the correct answer is option 'D' - All of these.
Disjoint Sets:
Disjoint sets are sets that have no elements in common. In other words, the intersection of two disjoint sets is an empty set.
Option 'A':
A - B represents the set of elements that are in set A but not in set B. A ∩ B represents the set of elements that are common to both set A and set B. So, A - (A ∩ B) represents the elements that are in set A but not in the intersection of sets A and B. This is equivalent to A - B.
Option 'B':
B - A represents the set of elements that are in set B but not in set A. Aᶜ represents the complement of set A. So, B ∩ Aᶜ represents the set of elements that are in set B and not in set A. This is equivalent to B - A.
Option 'C':
A ∩ B represents the set of elements that are common to both set A and set B. (A-B) represents the set of elements that are in set A but not in set B. (A-B) ∩ B represents the set of elements that are in set A but not in set B, and also in set B. This is equivalent to A ∩ B.
Conclusion:
Since all the given options correctly represent the operations on disjoint sets A and B, the correct answer is option 'D' - All of these.
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Community Answer
If A and. B are two disjoint sets, then which one of the following is ...
Since, A ∩ B = φ (given)
So, A - B = A - ( A ∩ B )
(Since, A - B = A)
Now, B - A' = φ
and B ∩ A = φ
or B ‘- A ' = B ∩ A
and (A- B ) ∩ B = A ∩ B
So, option (d) is correct.
So, A - B = A - ( A ∩ B )
(Since, A - B = A)
Now, B - A' = φ
and B ∩ A = φ
or B ‘- A ' = B ∩ A
and (A- B ) ∩ B = A ∩ B
So, option (d) is correct.
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