Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2008
Hard
If P, Q, R are subsets of the universal set U, then (P∩Q∩R) ∪ (Pᶜ∩Q∩R) ∪ Qᶜ ∪ Rᶜ is
- AQᶜ ∪ Rᶜ
- BP ∪ Qᶜ ∪ Rᶜ
- CPᶜ ∪ Qᶜ ∪ Rᶜ
- U
Explanation
(P∩Q∩R) ∪ (Pᶜ∩Q∩R) = (P∪Pᶜ)∩Q∩R = Q∩R. So the expression becomes (Q∩R) ∪ Qᶜ ∪ Rᶜ = (Q∩R) ∪ (Q∩R)ᶜ [by De Morgan, Qᶜ∪Rᶜ=(Q∩R)ᶜ] = U.
Source: GATE CS 2008 (2008)
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