Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Set ( a ∪ B ′ ) ′ ∪ ( B ∩ C ) is Equal to - Mathematics

MCQ

The set  \[\left( A \cup B' \right)' \cup \left( B \cap C \right)\] is equal to

 

Options

  • (a)  \[A' \cup B \cup C\]

  •  (b)  \[A' \cup B\]

     

  •  (c) \[A' \cup c\]

     

  •  (d)  \[A' \cap B\]

     

  • (e) n/a

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Solution

\[\left( A \cup B' \right)' \cup \left( B \cap C \right)\]

\[ = \left[ A' \cap \left( B' \right)' \right] \cup \left( B \cap C \right) \left( \text{ De Morgan law }  \right)\]

\[ = \left( A' \cap B \right) \cup \left( B \cap C \right)\]

\[ = \left( A' \cup C \right) \cap B \left( \text{ Distributive law}  \right)\]

Notes

Disclaimer: The question seems to be incorrect or there is some printing mistake in the question. The options given in the question does not match with the answer.

Concept: Equal Sets
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Q 29 | Page 51
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