1

GATE CSE 2001

MCQ (Single Correct Answer)

+2

-0.6

Let $$f:\,A\, \to B$$ be a function, and let E and F be subsets of A. Consider the following statements about images.

$$S1:\,f\,\left( {E\, \cup \,F} \right)\, = \,f\left( E \right)\, \cup \,f\,\left( F \right)$$

$$S2:\,f\,\left( {E\, \cap \,F} \right)\, = \,f\left( E \right)\, \cap \,f\,\left( F \right)$$

Which of the following is true about S1 and S2?

2

GATE CSE 2000

MCQ (Single Correct Answer)

+2

-0.6

Let P(S) denote the power set of a set S. Which of the following is always true?

3

GATE CSE 2000

MCQ (Single Correct Answer)

+2

-0.6

A relation R is defined on the set of integers as zRy if f (x + y) is even. Which of the following statements is true?

4

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.

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 3 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2014 Set 2 (1)
GATE CSE 2014 Set 3 (2)
GATE CSE 2014 Set 1 (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