GATE CSE 2014 Set 3 | Mathematical Logic Question 16 | Discrete Mathematics

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GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

-0.6

The CORRECT formula for the sentence, "not all rainy days are cold" is

$$\forall d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$

$$\forall d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$

$$\exists d\left( { \sim Rainy\left( d \right) \to Cold\left( d \right)} \right)$$

$$\exists d\left( {Rainy\left( d \right) \wedge \sim Cold\left( d \right)} \right)$$

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 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

Undecidability Finite Automata and Regular Language Push Down Automata and Context Free Language 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

Trees Hashing Arrays Linked List Graphs Stacks and Queues

Computer Networks

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

Software Engineering

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Web Technologies

General Aptitude

Numerical Ability Logical Reasoning Verbal Ability

Discrete Mathematics

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

Programming Languages

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

Computer Organization

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