1
GATE CSE 2000
+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?
A
R is not an equivalence relation
B
R is an equivalence relation having 1 equivalence class
C
R is an equivalence relation having 2 equivalence classes
D
R is an equivalence relation having 3 equivalence classes
2
GATE CSE 2000
+2
-0.6
Let P(S) denote the power set of a set S. Which of the following is always true?
A
$$P\,(P(S))\, = P\,(S)$$
B
$$P\,(S)\, \cap \,P\,(P\,(S)) = \{ \emptyset \}$$
C
$$P\,(S)\,\, \cap \,\,S = P\,(S)$$
D
$$S\,\, \notin \,P(S)$$
3
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.

4
GATE CSE 1998
+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
A
Reflexive, symmetric and transitive
B
Neither reflexive, nor irreflexive but transitive
C
Irreflexive, symmetric and transitive
D
Irreflexive and antisymmetric
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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