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If A, B and C are any three sets , then A – (B∩C) is equal to
- a)(A – B) ∩ C
- b)(A – B) ∪ C
- c)(A – B) ∩ (A – C)
- d)(A – C) ∩ (B – C)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If A, B and C are any three sets , then A – (B∩C) is equal...
Set S of odd positive an odd integer less than 10 is {1, 3, 5, 7, 9}. Then, Cardinality of set S = |S| which is 5.
Community Answer
If A, B and C are any three sets , then A – (B∩C) is equal...
Explanation:
To understand the given expression, let's break it down step by step.
Step 1: A (BC)
In this expression, BC represents the intersection of sets B and C. It means that only the elements common to both sets B and C will be considered.
Step 2: A (BC)
Now, we take the intersection of set A with the result of step 1 (BC). It means that we consider only the elements common to set A and the result of step 1.
Step 3: (A B) C
In this expression, A B represents the intersection of sets A and B. It means that only the elements common to both sets A and B will be considered.
Step 4: (A B) C
Now, we take the intersection of the result of step 3 (A B) with set C. It means that we consider only the elements common to the result of step 3 and set C.
Step 5: Comparing Steps 2 and 4
We need to compare the results of step 2 (A (BC)) and step 4 ((A B) C) to determine if they are equal.
Step 6: Proof of Equality
To prove the equality, we need to show that any element present in the result of step 2 (A (BC)) is also present in the result of step 4 ((A B) C), and vice versa.
Step 7: Element in A (BC) is also in (A B) C
Let x be an arbitrary element in set A (BC). This means that x is both in set A and in the intersection of sets B and C.
Since x is in set A, it is also in the intersection of sets A and B (A B).
And since x is in the intersection of sets B and C, it is also in the intersection of the result of step 3 ((A B) C) and set C.
Therefore, x is in both A (BC) and (A B) C.
Step 8: Element in (A B) C is also in A (BC)
Let y be an arbitrary element in the result of step 4 ((A B) C). This means that y is both in the intersection of sets A and B ((A B)) and in set C.
Since y is in the intersection of sets A and B, it is also in set A.
And since y is in set C, it is also in the intersection of set A and the result of step 1 (BC).
Therefore, y is in both (A B) C and A (BC).
Step 9: Conclusion
Since every element in A (BC) is also in (A B) C, and vice versa, we can conclude that A (BC) is equal to (A B) C.
Therefore, the correct answer is option 'B' - (A B) C.
To understand the given expression, let's break it down step by step.
Step 1: A (BC)
In this expression, BC represents the intersection of sets B and C. It means that only the elements common to both sets B and C will be considered.
Step 2: A (BC)
Now, we take the intersection of set A with the result of step 1 (BC). It means that we consider only the elements common to set A and the result of step 1.
Step 3: (A B) C
In this expression, A B represents the intersection of sets A and B. It means that only the elements common to both sets A and B will be considered.
Step 4: (A B) C
Now, we take the intersection of the result of step 3 (A B) with set C. It means that we consider only the elements common to the result of step 3 and set C.
Step 5: Comparing Steps 2 and 4
We need to compare the results of step 2 (A (BC)) and step 4 ((A B) C) to determine if they are equal.
Step 6: Proof of Equality
To prove the equality, we need to show that any element present in the result of step 2 (A (BC)) is also present in the result of step 4 ((A B) C), and vice versa.
Step 7: Element in A (BC) is also in (A B) C
Let x be an arbitrary element in set A (BC). This means that x is both in set A and in the intersection of sets B and C.
Since x is in set A, it is also in the intersection of sets A and B (A B).
And since x is in the intersection of sets B and C, it is also in the intersection of the result of step 3 ((A B) C) and set C.
Therefore, x is in both A (BC) and (A B) C.
Step 8: Element in (A B) C is also in A (BC)
Let y be an arbitrary element in the result of step 4 ((A B) C). This means that y is both in the intersection of sets A and B ((A B)) and in set C.
Since y is in the intersection of sets A and B, it is also in set A.
And since y is in set C, it is also in the intersection of set A and the result of step 1 (BC).
Therefore, y is in both (A B) C and A (BC).
Step 9: Conclusion
Since every element in A (BC) is also in (A B) C, and vice versa, we can conclude that A (BC) is equal to (A B) C.
Therefore, the correct answer is option 'B' - (A B) C.
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If A, B and C are any three sets , then A – (B∩C) is equal toa)(A – B)∩ Cb)(A – B)∪ Cc)(A – B)∩ (A – C)d)(A – C)∩ (B – C)Correct answer is option 'B'. Can you explain this answer?
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