Question:
Show that if \(A ⊂ B\), then \(C – B ⊂ C – A.\)
Show that if \(A ⊂ B\), then \(C – B ⊂ C – A.\)
Updated On: Oct 23, 2023
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Solution and Explanation
Let \(A ⊂ B \)
To show: \(C – B ⊂ C – A \)
Let \(x ∈ C – B \)
\(⇒ x ∈ C\) and \(x ∉ B \)
\(⇒ x ∈ C \) and \(x ∉ A [A ⊂ B] \)
\(⇒ x ∈ C – A \)
\(∴ C – B ⊂ C – A\)
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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.
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- It is denoted as “A ∩ B”
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- 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”