1
GATE CSE 1995
+2
-0.6
Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then
A
A is closed under * but $$< A,\,* >$$ is not a semigroup.
B
$$< A,\,* >$$ is a semigroup but not a monoid.
C
$$< A,\,* >$$ is a monoid but not a group.
D
$$< A,\,* >$$ is a group but not an abelian group
2
GATE CSE 1994
+2
-0.6
Some group (G, o) is known to be abelian. Then, which one of the following is true for G?
A
$$g = {g^{ - 1}}\,$$ for every $$g\, \in \,G$$.
B
$$g = {g^{ 2}}\,$$ for every $$g\, \in \,G$$.
C
$${(goh)^2} = \,{g^2}\,o\,\,{h^2}$$ for every g, $$h\, \in \,G$$.
D
G is of finite order.
3
GATE CSE 1989
Fill in the Blanks
+2
-0
The transitive closure of the relation
$$\left\{ {\left( {1,2} \right)\left( {2,3} \right)\left( {3,4} \right)\left( {5,4} \right)} \right\}$$
on the set $$A = \left\{ {1,2,3,4,5} \right\}$$ is ________ .
4
GATE CSE 1988
Fill in the Blanks
+2
-0
The complement(s) of the element 'a' in the lattice shown in Fig. is (are) ........... . 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
EXAM MAP
Joint Entrance Examination