1

GATE CSE 2004

MCQ (Single Correct Answer)

+1

-0.3

Consider the binary relation: $$S = \left\{ {\left( {x,y} \right)|y = x + 1\,\,and\,\,x,y \in \left\{ {0,1,2,...} \right\}} \right\}$$

The reflexive transitive closure of $$S$$ is

2

GATE CSE 2004

MCQ (Single Correct Answer)

+1

-0.3

The number of different $$n$$ $$x$$ $$n$$ symmetric matrices with each elements being either $$0$$ or $$1$$ is (Note: power ($$2,$$ $$x$$) is same as $${2^x}$$)

3

GATE CSE 2004

MCQ (Single Correct Answer)

+1

-0.3

Let $${R_1}$$ be a relation from $$A = \left\{ {1,3,5,7} \right\}$$ to $$B = \left\{ {2,4,6,8} \right\}$$ and $${R_2}$$ be another relation from $$B$$ to $$C$$ $$ = \left\{ {1,2,3,4} \right\}$$ as defined below:

i) An element $$x$$ in $$A$$ is related to an element $$y$$ in $$B$$ (under $${R_1}$$) if $$ x + y $$ is divisible by $$3$$.

ii) An element EExEE in $$B$$ is related to an elements $$y$$ in $$C$$ (under $${R_2}$$) if $$x + y$$ is even but not divisible by $$3$$.

Which is the composite relation $$R1R2$$ from $$A$$ to $$C$$?

4

GATE CSE 2001

MCQ (Single Correct Answer)

+1

-0.3

Consider the following relations:

$${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is even over the set of integers

$${R_2}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is odd over the set of integers

$${R_3}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,a.b > 0$$ over the set of non-zero rational numbers

$${R_4}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left| {a - b} \right| \le 2$$ over the set of natural numbers

$${R_1}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is even over the set of integers

$${R_2}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left( {a + b} \right)$$ is odd over the set of integers

$${R_3}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,a.b > 0$$ over the set of non-zero rational numbers

$${R_4}\,\,\left( {a,\,\,b} \right)\,\,\,iff\,\,\left| {a - b} \right| \le 2$$ over the set of natural numbers

Which of the following statements is correct?

Questions Asked from Set Theory & Algebra (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2020 (2)
GATE CSE 2019 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2015 Set 1 (1)
GATE CSE 2014 Set 3 (1)
GATE CSE 2013 (2)
GATE CSE 2010 (2)
GATE CSE 2009 (2)
GATE CSE 2008 (1)
GATE CSE 2007 (2)
GATE CSE 2006 (4)
GATE CSE 2005 (4)
GATE CSE 2004 (3)
GATE CSE 2001 (1)
GATE CSE 1999 (1)
GATE CSE 1998 (3)
GATE CSE 1997 (1)
GATE CSE 1996 (4)
GATE CSE 1995 (2)
GATE CSE 1993 (2)
GATE CSE 1987 (2)

GATE CSE Subjects

Discrete Mathematics

Programming Languages

Theory of Computation

Operating Systems

Computer Organization

Database Management System

Data Structures

Computer Networks

Algorithms

Compiler Design

Software Engineering

Web Technologies

General Aptitude