De Morgan Laws of Propositional Logic MCQ Quiz - Objective Question with Answer for De Morgan Laws of Propositional Logic - Download Free PDF
Last updated on Mar 17, 2025
Latest De Morgan Laws of Propositional Logic MCQ Objective Questions
Top De Morgan Laws of Propositional Logic MCQ Objective Questions
De Morgan Laws of Propositional Logic Question 1:
Match the following.
|
List-1 |
List -2 |
|
(I) (X’)’ |
(A) De Morgan law |
|
(II) (X + Y)’=X’.Y’ |
(B) Involution |
|
(III) X(X+Y) = X |
(C) Distributive |
|
(IV) X + YZ = (X +Y) (X+Z) |
(D) Absorption |
Answer (Detailed Solution Below)
Option 2 : I – B, II – A, III –D, IV - C
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De Morgan Laws of Propositional Logic Question 1 Detailed Solution
(X’)’ = X → involution law.
X + Y)’=X’.Y’ → De Morgan Law
X(X+Y) = X + XY = X → Absorption law
X + YZ = (X +Y) (X+Z) → Distributive law
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De Morgan Laws of Propositional Logic Question 2:
Which of the following is equivalent to \(\sim ∃(P(x)∧Q(y))\)?
Answer (Detailed Solution Below)
Option 3 : \(∀x(P(x)→\sim Q(y))\)
De Morgan Laws of Propositional Logic Question 2 Detailed Solution
The correct answer is option 3 i.e. \(∀x(P(x)→\sim Q(y))\)
Proof: \(\sim ∃(P(x)∧Q(y))\)
\(∀x\sim (P(x)∧Q(y))\)
\(∀x(\sim P(x)∨\sim Q(y))\)
\(∀x(P(x)→\sim Q(y))\)
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