GATE CSE 2005 | Set Theory & Algebra Question 56 | Discrete Mathematics

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let f: $$\,B \to \,C$$ and g: $$\,A \to \,B$$ be two functions and let h = fog. Given that h is an onto function which one of the following is TRUE?

f and g should both be onto functions

f should be onto but g need not be into

g should be onto but f need not be onto

both f and need not be onto

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let R and S be any two equivalence relations on a non-emply set A. Which one of the following statements is TRUE?

$$R\, \cup \,S\,,\,R\, \cap \,S$$ are both equivalence relations

$$R\, \cup \,S\,$$ is an equivalence relations

$$R\, \cap \,S$$ is an equivalence relations

Neither $$R\, \cup \,S\,$$ nor $$R\, \cap \,S$$ is an equivalence relation

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

The inclusion of which of the following sets into

S = { {1, 2}, 1, 2, 3}, {1, 3, 5}, {1, 2, 4},
{1, 2, 3, 4, 5} }
Is necessary and sufficient to make S a complete lattice under the partial order defined by set containment?

{1}

{1}, {2, 3}

{1}, {1, 3}

{1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

The following is the incomplete operation table of a 4-element group. GATE CSE 2004 Discrete Mathematics - Set Theory & Algebra Question 103 English

GATE CSE 2004 Discrete Mathematics - Set Theory & Algebra Question 103 English

The last row of the table is

$$\matrix{ c & a & e & b \cr } $$

$$\matrix{ c & b & a & e \cr } $$

$$\matrix{ c & b & e & a \cr } $$

$$\matrix{ c & e & a & b \cr } $$

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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

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

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

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

Programming Languages

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

Computer Organization

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