Propositional Logic and Logical Equivalence Previous Year Questions (PYQs) for GATE DA: 3+ Solved Questions with Step-by-Step Solutions

Solve 3+ Propositional Logic and Logical Equivalence previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Propositional Logic

Chapter Journey: Propositional Logic

Step 1: The Language of Logic

Translating English to Propositional Logic
Conditional and Biconditional Statements
Understanding Necessary vs. Sufficient Conditions

Step 2: The Mechanics of Truth

Truth Tables and Tautologies
Logical Equivalence and Algebraic Simplification
Fundamental Laws of Logic (De Morgan's, Contrapositive)

Step 3: Exam Mastery

Decoding Complex Word Problems
Identifying Equivalent Propositions Quickly
Avoiding Common Logical Fallacies

The Core of Logical Reasoning

What is Propositional Logic?
Propositional logic is the study of propositions (declarative statements that are either True or False) and how they combine using logical connectives.

Symbol	Name	Meaning
$\land$	Conjunction	AND (Both must be true)
$\lor$	Disjunction	OR (At least one must be true)
$\neg$	Negation	NOT (Flips the truth value)
$\to$	Implication	IMPLIES (If... then...)
$⟺$	Biconditional	IF AND ONLY IF (Same truth value)

The Goal:
To take messy, ambiguous English sentences, convert them into precise symbolic logic, and use mathematical rules to determine their truth values or simplify them.

Propositional Logic and Logical Equivalence: Solved Questions with Step-by-Step Explanations (3 Problems)

Question 1 · Analytical Aptitude MCQ

Let

p

and

q

be any two propositions. Consider the following propositional statements.

S_{1} : p \to q, S_{2} : \neg p \land q, S_{3} : \neg p \lor q, S_{4} : \neg p \lor \neg q,

where

\land

denotes conjunction (AND operation),

\lor

denotes disjunction (OR operation), and

\neg

denotes negation (NOT operation). Which one of the following options is correct?
(Note:

\equiv

denotes logical equivalence)

A.
$S_{1} \equiv S_{3}$
B.
$S_{2} \equiv S_{3}$
C.
$S_{2} \equiv S_{4}$
D.
$S_{1} \equiv S_{4}$

Question 2 · Analytical Aptitude MCQ

Assume that a Creative

(C)

person will Succeed

(S)

if the person is also Disciplined

(D)

, but will not succeed otherwise. Now, consider the following statements:

(i)

C \land S \Leftrightarrow D

(ii)

C \Rightarrow (S ⟺ D)

(iii)

C \Leftrightarrow ((D \Rightarrow S) \lor \neg S)

Which of the following options is correct?

A.
Both (i) and (ii) are TRUE
B.
Only (ii) is TRUE
C.
Both (ii) and (iii) are TRUE
D.
Only (iii) is TRUE

Question 3 · Analytical Aptitude MSQ

Let

x

and

y

be two propositions. Which of the following statements is a tautology
/are tautologies?

A.
$(\neg x \land y) ⟹ (y ⟹ x)$
B.
$(x \land \neg y) ⟹ (\neg x ⟹ y)$
C.
$(\neg x \land y) ⟹ (\neg x ⟹ y)$
D.
$(x \land \neg y) ⟹ (y ⟹ x)$

Propositional Logic and Logical Equivalence Previous Year Questions (PYQs) for GATE DA: 3+ Solved Questions with Step-by-Step Solutions

Chapter Roadmap: Propositional Logic

Chapter Journey: Propositional Logic

The Core of Logical Reasoning

Propositional Logic and Logical Equivalence: Solved Questions with Step-by-Step Explanations (3 Problems)

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