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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