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
EXAM MAP
Medical
NEET