Let $P$ be the relation defined on the set of all real numbers such that
$P = \left\{ {\left( {a,b} \right):{{\sec }^2}\,a - {{\tan }^2}\,b = 1\,} \right\}$. Then $P$ is
Let $P$ be the relation defined on the set of all real numbers such that
$P = \left\{ {\left( {a,b} \right):{{\sec }^2}\,a - {{\tan }^2}\,b = 1\,} \right\}$. Then $P$ is
- [JEE MAIN 2014]
- A
reflexive and symmetric but not transitive
- B
reflexive and transitive but not symmetric
- C
symmetric and transitive but not reflexive
- D
an equivalence relation
Similar Questions
The relation "is subset of" on the power set $P(A)$ of a set $A$ is
The relation "is subset of" on the power set $P(A)$ of a set $A$ is
Among the relations $S =\left\{( a , b ): a , b \in R -\{0\}, 2+\frac{ a }{ b } > 0\right\}$ And $T =\left\{( a , b ): a , b \in R , a ^2- b ^2 \in Z \right\}$,
Among the relations $S =\left\{( a , b ): a , b \in R -\{0\}, 2+\frac{ a }{ b } > 0\right\}$ And $T =\left\{( a , b ): a , b \in R , a ^2- b ^2 \in Z \right\}$,
- [JEE MAIN 2023]
Let $R$ and $S$ be two equivalence relations on a set $A$. Then
Let $R$ and $S$ be two equivalence relations on a set $A$. Then
Given a non empty set $X$, consider $P ( X )$ which is the set of all subsets of $X$.
Define the relation $R$ in $P(X)$ as follows :
For subsets $A,\, B$ in $P(X),$ $ARB$ if and only if $A \subset B .$ Is $R$ an equivalence relation on $P ( X ) ?$ Justify your answer.
Given a non empty set $X$, consider $P ( X )$ which is the set of all subsets of $X$.
Define the relation $R$ in $P(X)$ as follows :
For subsets $A,\, B$ in $P(X),$ $ARB$ if and only if $A \subset B .$ Is $R$ an equivalence relation on $P ( X ) ?$ Justify your answer.
Let $A=\{1,2,3\} .$ Then number of equivalence relations containing $(1,2)$ is
Let $A=\{1,2,3\} .$ Then number of equivalence relations containing $(1,2)$ is