28
MCQ (Single Correct Answer)
Let $T$ be the set of all triangles in the Euclidean plane and let a relation $R$ on $T$ be defined as $a R b$, if $a$ is congruent to $b, \forall a, b \in T$. Then, $R$ is
A
reflexive but not transitive
B
transitive but not symmetric
C
equivalence
D
None of these
29
MCQ (Single Correct Answer)
Consider the non-empty set consisting of children in a family and a relation $R$ defined as $a R b$, if $a$ is brother of $b$. Then, $R$ is
A
symmetric but not transitive
B
transitive but not symmetric
C
neither symmetric nor transitive
D
both symmetric and transitive
30
MCQ (Single Correct Answer)
The maximum number of equivalence relations on the set $A=\{1,2,3\}$ are
A
1
B
2
C
3
D
5
31
MCQ (Single Correct Answer)
If a relation $R$ on the set $\{1,2,3\}$ be defined by $R=\{(1,2)\}$, then $R$ is
A
reflexive
B
transitive
C
symmetric
D
None of these
32
MCQ (Single Correct Answer)
Let us define a relation $R$ in $R$ as $a R b$ if $a \geq b$. Then, $R$ is
A
an equivalence relation
B
reflexive, transitive but not symmetric
C
symmetric, transitive but not reflexive
D
neither transitive nor reflexive but symmetric