Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# 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

#### 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