1
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
2
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

3
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.

4
GATE CSE 1996
+2
-0.6
Let R be a non-emply relation on a collection of sets defined by $${A^R}\,B$$ if and only if $$A\, \cap \,B\, = \,\phi$$. Then, (pick the true statement)
A
R is reflexive and transitive
B
R is symmetric and not transitive
C
R is an equivalence relation
D
R is not reflexive and not symmetric
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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