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Discrete Mathematics
Set Theory & Algebra
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1
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following Boolean expressions is NOT A tautology?
A
$$\left( {\left( {a \to b} \right) \wedge \left( {b \to c} \right)} \right) \to \left( {a \to c} \right)$$
B
$$\left( {a \leftrightarrow c} \right) \to \left( { \sim b \to \left( {a \wedge c} \right)} \right)$$
C
$$\left( {a \wedge b \wedge c} \right) \to \left( {c \vee a} \right)$$
D
$$A \to \left( {b \to a} \right)$$
2
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following propositional logic formulas is TRUE when exactly two of $$p, q,$$ and $$r$$ are TRUE?
A
$$\left( {\left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
B
$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
C
$$\left( {\left( {p \to q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$
D
$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \wedge \left( {p \wedge q \wedge \sim r} \right)$$
3
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
What is the logical translation of the following statement?
"None of my friends are perfect."
A
$$\exists x\left( {F\left( x \right) \wedge \neg P\left( x \right)} \right)$$
B
$$\exists x\left( {\neg F\left( x \right) \wedge P\left( x \right)} \right)$$
C
$$\exists x\left( {\neg F\left( x \right) \wedge \neg P\left( x \right)} \right)$$
D
$$\neg \exists x\left( {F\left( x \right) \wedge P\left( x \right)} \right)$$
4
GATE CSE 2013
MCQ (More than One Correct Answer)
+2
-0
Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$
A
$$\forall x\left( {\exists z\left( {\neg \beta } \right) \to \forall y\left( \alpha \right)} \right)$$
B
$$\forall x\left( {\forall z\left( \beta \right) \to \exists y\left( {\neg \alpha } \right)} \right)$$
C
$$\forall x\left( {\forall y\left( \alpha \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
D
$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$
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Questions Asked from Marks 2
GATE CSE 2025 Set 1 (1) GATE CSE 2020 (1) GATE CSE 2019 (1) GATE CSE 2018 (1) GATE CSE 2016 Set 2 (1) GATE CSE 2015 Set 2 (1) GATE CSE 2014 Set 3 (1) GATE CSE 2014 Set 2 (1) GATE CSE 2014 Set 1 (1) GATE CSE 2013 (2) GATE CSE 2011 (1) GATE CSE 2010 (1) GATE CSE 2009 (3) GATE CSE 2008 (5) GATE CSE 2007 (1) GATE CSE 2006 (5) GATE CSE 2005 (3) GATE CSE 2004 (2) GATE CSE 2003 (1) GATE CSE 2000 (1) GATE CSE 1996 (1) GATE CSE 1995 (1) GATE CSE 1994 (1) GATE CSE 1990 (1)
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization