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Statement-1 If U is universal set and B ...

Statement-1 If U is universal set and B = U - A, then n(B) = n(U) - n(A).
Statement-2 For any three arbitrary sets A, B and C, if C = A - B, then n(C ) = n(A) - n(B).

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To determine the truth of the two statements provided, we will analyze each statement step by step. ### Step 1: Analyze Statement 1 **Statement 1:** If \( U \) is the universal set and \( B = U - A \), then \( n(B) = n(U) - n(A) \). 1. **Understanding the Sets**: - Let \( U \) be the universal set containing all possible elements. - Let \( A \) be a subset of \( U \). - The set \( B \) is defined as the complement of \( A \) in \( U \), which means \( B \) contains all elements in \( U \) that are not in \( A \). 2. **Counting Elements**: - The total number of elements in the universal set \( U \) is denoted as \( n(U) \). - The number of elements in set \( A \) is denoted as \( n(A) \). - Since \( B \) contains all elements of \( U \) that are not in \( A \), we can express the number of elements in \( B \) as: \[ n(B) = n(U) - n(A) \] 3. **Conclusion for Statement 1**: - The statement is true because it correctly describes the relationship between the universal set, a subset, and its complement. ### Step 2: Analyze Statement 2 **Statement 2:** For any three arbitrary sets \( A, B, \) and \( C \), if \( C = A - B \), then \( n(C) = n(A) - n(B) \). 1. **Understanding the Sets**: - Here, \( C \) is defined as the difference between sets \( A \) and \( B \), meaning \( C \) contains all elements that are in \( A \) but not in \( B \). 2. **Counting Elements**: - The number of elements in set \( A \) is \( n(A) \). - The number of elements in set \( B \) is \( n(B) \). - However, \( n(C) \) should actually account for the elements in \( A \) that are not in \( B \). This can be expressed as: \[ n(C) = n(A) - n(A \cap B) \] - Therefore, the correct expression for \( n(C) \) is not simply \( n(A) - n(B) \) because \( n(B) \) does not account for the overlap between \( A \) and \( B \). 3. **Conclusion for Statement 2**: - The statement is false because it incorrectly assumes that the number of elements in \( C \) can be calculated by simply subtracting the number of elements in \( B \) from \( A \) without considering the intersection of \( A \) and \( B \). ### Final Conclusion - **Statement 1** is **True**. - **Statement 2** is **False**.

To determine the truth of the two statements provided, we will analyze each statement step by step. ### Step 1: Analyze Statement 1 **Statement 1:** If \( U \) is the universal set and \( B = U - A \), then \( n(B) = n(U) - n(A) \). 1. **Understanding the Sets**: - Let \( U \) be the universal set containing all possible elements. - Let \( A \) be a subset of \( U \). ...
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