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 12, 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

  1. I – D, II – A, III – B, IV - C
  2. I – B, II – A, III –D, IV - C
  3. I – B, II – D, III – A, IV - C
  4. I – C, II – A, III – D, IV - B

Answer (Detailed Solution Below)

Option 2 : I – B, II – A, III –D, IV - C

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

De Morgan Laws of Propositional Logic Question 2:

Which of the following is equivalent to \(\sim ∃(P(x)∧Q(y))\)?

  1. \(∀\sim x(P(x)→ \sim Q(y))\)
  2. \(∀x(P(x)⋁~Q(y))\)
  3. \(∀x(P(x)→\sim Q(y))\)
  4. \(∃(P(x)∧Q(y))\)

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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