GATE CSE 2005 | Set Theory & Algebra Question 48 | 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 following is the incomplete operation table of a 4-element group. GATE CSE 2004 Discrete Mathematics - Set Theory & Algebra Question 96 English

The last row of the table is

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

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

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

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

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}

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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

Theory of Computation

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

Operating Systems

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

Digital Logic

K Maps Boolean Algebra Combinational Circuits Number Systems Sequential Circuits

Computer Organization

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

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

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

Algorithms

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

Compiler Design

Lexical Analysis Parsing Syntax Directed Translation Code Generation and Optimization

Software Engineering

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