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The set (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′ is equal to 

  1. B ∩ C′
  2. A ∩ C
  3. B ∪ C′
  4. A ∩ C′

Answer (Detailed Solution Below)

Option 1 : B ∩ C′

Detailed Solution

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Calculation:

Given (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′

⇒ (A ∪ B ∪ C) ∩ (A ∩ B′ ∩ C′)′ ∩ C′

⇒ ((A ∪ B ∪ C) ∩ (A' ∪ B ∪ C)) ∩ C′

⇒ ((A ∩ A') ∪ (B ∪ C)) ∩ C' .

⇒ (ϕ ∪ (B ∪ C)) ∩ C'

⇒ (B ∪ C) ∩ C'

⇒ (B ∩ C') ∪  (C ∩ C')

⇒ (B ∩ C') ∪ ϕ 

⇒ B ∩ C'

Required equivalent is B ∩ C' .

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