1
GATE CSE 2010
+1
-0.3
What is the possible number of reflexive relations on a set $$5$$ elements?
A
210
B
215
C
220
D
225
2
GATE CSE 2010
+1
-0.3
Consider the set $$S = \left\{ {1,\,\omega ,\,{\omega ^2}} \right\},$$ where $$\omega$$ and $${{\omega ^2}}$$, are cube roots of unity. If $$*$$ denotes the multiplication operation, the structure $$\left\{ {S,\, * } \right\}$$ forms
A
a group
B
a ring
C
an integral domain
D
a field
3
GATE CSE 2009
+1
-0.3
Which one of the following in NOT necessarily a property of Group?
A
Commutativity
B
Associativity
C
Existence of inverse for every element
D
Existence of identity
4
GATE CSE 2009
+1
-0.3
consider the binary relation $$R = \left\{ {\left( {x,y} \right),\,\left( {x,z} \right),\,\left( {z,x} \right),\,\left( {z,y} \right)} \right\}$$ on the set $$\left\{ {x,\,y,\,z} \right\}$$. which one of the following is TRUE?
A
$$R$$ is symmetric but $$NOT$$ antisymmetric
B
$$R$$ is NOT symmetric but antisymmetric
C
$$R$$ is both symmetric and antisymmetric.
D
$$R$$ is neither symmetric nor antisymmetric.
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