GATE CSE 2014 Set 1 | Mathematical Logic Question 20 | Discrete Mathematics

GATE CSE 2014 Set 1

MCQ (Single Correct Answer)

-0.6

Which one of the following propositional logic formulas is TRUE when exactly two of $$p, q,$$ and $$r$$ are TRUE?

$$\left( {\left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$

$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$

$$\left( {\left( {p \to q} \right) \wedge r} \right) \vee \left( {p \wedge q \wedge \sim r} \right)$$

$$\left( { \sim \left( {p \leftrightarrow q} \right) \wedge r} \right) \wedge \left( {p \wedge q \wedge \sim r} \right)$$

GATE CSE 2014 Set 2

MCQ (Single Correct Answer)

-0.6

Which one of the following Boolean expressions is NOT A tautology?

$$\left( {\left( {a \to b} \right) \wedge \left( {b \to c} \right)} \right) \to \left( {a \to c} \right)$$

$$\left( {a \leftrightarrow c} \right) \to \left( { \sim b \to \left( {a \wedge c} \right)} \right)$$

$$\left( {a \wedge b \wedge c} \right) \to \left( {c \vee a} \right)$$

$$A \to \left( {b \to a} \right)$$

GATE CSE 2013

MCQ (Single Correct Answer)

-0.6

What is the logical translation of the following statement?
"None of my friends are perfect."

$$\exists x\left( {F\left( x \right) \wedge \neg P\left( x \right)} \right)$$

$$\exists x\left( {\neg F\left( x \right) \wedge P\left( x \right)} \right)$$

$$\exists x\left( {\neg F\left( x \right) \wedge \neg P\left( x \right)} \right)$$

$$\neg \exists x\left( {F\left( x \right) \wedge P\left( x \right)} \right)$$

GATE CSE 2013

MCQ (More than One Correct Answer)

-0

Which one of the following is NOT logically equivalent to $$\neg \exists x\left( {\forall y\left( \alpha \right) \wedge \left( {\forall z\left( \beta \right)} \right)} \right)?$$

$$\forall x\left( {\exists z\left( {\neg \beta } \right) \to \forall y\left( \alpha \right)} \right)$$

$$\forall x\left( {\forall z\left( \beta \right) \to \exists y\left( {\neg \alpha } \right)} \right)$$

$$\forall x\left( {\forall y\left( \alpha \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

$$\forall x\left( {\exists y\left( {\neg \alpha } \right) \to \exists z\left( {\neg \beta } \right)} \right)$$

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GATE CSE Subjects

Theory of Computation

Finite Automata and Regular Language Push Down Automata and Context Free Language Undecidability Recursively Enumerable Language and Turing Machine

Operating Systems

Process Concepts and Cpu Scheduling Synchronization and Concurrency Deadlocks Memory Management File System IO and Protection

Algorithms

Complexity Analysis and Asymptotic Notations Searching and Sorting Divide and Conquer Method Greedy Method Dynamic Programming P and NP Concepts

Digital Logic

K Maps Boolean Algebra Combinational Circuits Number Systems Sequential Circuits

Database Management System

Er Diagrams Functional Dependencies and Normalization Structured Query Language Relational Algebra Transactions and Concurrency File Structures and Indexing

Data Structures

Arrays Stacks and Queues Linked List Trees Graphs Hashing

Computer Networks

Concepts of Layering Data Link Layer and Switching Network Layer Application Layer Protocol Routing Algorithm TCP UDP Sockets and Congestion Control Lan Technologies and Wi-Fi Network Security

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

General Aptitude

Verbal Ability Logical Reasoning Numerical Ability

Discrete Mathematics

Set Theory & Algebra Linear Algebra Graph Theory Combinatorics Mathematical Logic Probability Calculus

Programming Languages

Basic of Programming Language Function and Recursion Pointer and Structure in C

Computer Organization

Computer Arithmetic Pipelining Machine Instructions and Addressing Modes Memory Interfacing IO Interface Alu Data Path and Control Unit Secondary Memory