1

GATE CSE 1999

Subjective

+2

-0

(a) Mr. X claims the following:

If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof.

"From xRy, using symmetry we get yRx. Now because R is transitive, xRy and yRx togethrer imply xRx. Therefore, R is reflextive."

Briefly point out the flaw in Mr. X' proof.

(b) Give an example of a relation R which is symmetric and transitive but not reflexive.

2

GATE CSE 1998

MCQ (Single Correct Answer)

+2

-0.6

The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is

3

GATE CSE 1998

Subjective

+2

-0

Let (A, *) be a semigroup. Furthermore, for every a and b in A, if $$a\, \ne \,b$$, then $$a\,*\,b \ne \,\,b\,*\,a$$.

(a) Show that for every a in A

a * a = a

(b) Show that for every a, b in A

a * b * a = a

(c) Show that for every a, b, c in A

a * b * c = a * c

4

GATE CSE 1998

Subjective

+2

-0

Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A

$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\} $$

(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$

(b) Draw the graph of the above equivalence relation.

Questions Asked from Set Theory & Algebra (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2024 Set 2 (1)
GATE CSE 2024 Set 1 (1)
GATE CSE 2023 (1)
GATE CSE 2021 Set 1 (1)
GATE CSE 2019 (1)
GATE CSE 2018 (1)
GATE CSE 2016 Set 2 (2)
GATE CSE 2016 Set 1 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2014 Set 1 (1)
GATE CSE 2014 Set 3 (2)
GATE CSE 2014 Set 2 (1)
GATE CSE 2012 (1)
GATE CSE 2009 (1)
GATE CSE 2007 (4)
GATE CSE 2006 (4)
GATE CSE 2005 (3)
GATE CSE 2004 (2)
GATE CSE 2002 (1)
GATE CSE 2001 (2)
GATE CSE 2000 (2)
GATE CSE 1999 (1)
GATE CSE 1998 (3)
GATE CSE 1996 (3)
GATE CSE 1995 (1)
GATE CSE 1994 (1)
GATE CSE 1989 (1)
GATE CSE 1988 (1)

GATE CSE Subjects

Theory of Computation

Operating Systems

Algorithms

Database Management System

Data Structures

Computer Networks

Software Engineering

Compiler Design

Web Technologies

General Aptitude

Discrete Mathematics

Programming Languages