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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

The set (A B C) (A B^ ′ C^ ′ ) ^ ′ is equal to

The set (A∪B∪C)∩(A∩B′∩C′)′\left(A \cup B \cup C\right) \cap {\left(A \cap B^{′} \cap C^{′}\right)}^{′} is equal to

Options

  1. AA∩BA \cap B
  2. BA∩C′A \cap C^{′}
  3. CB∪CB \cup C
  4. DB∩CB \cap C

Correct answer

C. B∪CB \cup C

Step-by-step solution

(A∪B∪C)∩(A∩B′∩C′)\left(A \cup B \cup C\right)\cap {\left(A \cap B^{′} \cap C^{′}\right)}^{′}<br/><br />=\left(A \cup B \cup C\right)\cap \left(A^{′} \cup B \cup C\right)<br/><br />= \left[ \left(A \cap A^{'}\right)\cup \left(B \cup C\right)\right]
=(ϕ∪B∪C)== \left(ϕ \cup B \cup C\right) =( B \cup C )$$
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