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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

For any two sets A and B, the values of [(A - B) B] ^ C is equal to

For any two sets AandA andB,thevaluesofthe values of{\left[\left(A - B\right) \cup B\right]}^{C} is equal to

Options

  1. AAC∩BCA^{C} \cap B^{C}
  2. BA∪BA \cup B
  3. CA−BA - B
  4. DB−AB - A

Correct answer

A. AC∩BCA^{C} \cap B^{C}

Step-by-step solution

(A−B)∪B=(A∩BC)∪B=(A∪B)∩(BC∪B)=(A∪B)∩(U)=A∪B\begin{array}{ll}( A - B ) \cup B = ( A \cap B^{C} ) \cup B \\ = ( A \cup B ) \cap ( B^{C} \cup B ) \\ = ( A \cup B ) \cap ( U ) \\ = A \cup B\end{array}
Hence,
[(A−B)∪B]C=(A∪B)C=AC∩BC{[ ( A - B ) \cup B ]}^{C} = {( A \cup B )}^{C} = A^{C} \cap B^{C}
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