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Question:
Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:
Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:
Updated On: Apr 25, 2024
- \(A\cup(B/C)=(A\cup B)/(A\cup C)\)
\((A/B)/C=A/(B\cup C)\)
- \((A\cup B)=A/B\)
- \(A/B=B/C\)
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The Correct Option is B
Solution and Explanation
The correct answer is option (B): \((A/B)/C=A/(B\cup C)\)
We know that if \(A\cup B=A\cup C\) and \(A\cap B=A\cap C\), then B=C which gives A\(\subset\)C
Hence, (A/B)/C=A/(B∪C)
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
1. Union of Sets:
- The union of sets lists the elements in set A and set B or the elements in both set A and set B.
- For example, {3,4} ∪ {1, 4} = {1, 3, 4}
- It is denoted as “A U B”
2. Intersection of Sets:
- Intersection of sets lists the common elements in set A and B.
- For example, {3,4} ∪ {1, 4} = {4}
- It is denoted as “A ∩ B”
3.Set Difference:
- Set difference is the list of elements in set A which is not present in set B
- For example, {3,4} - {1, 4} = {3}
- It is denoted as “A - B”
4.Set Complement:
- The set complement is the list of all elements present in the Universal set except the elements present in set A
- It is denoted as “U-A”
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