Consider set $A = \{1,2,3\}$ . Number of symmetric relations that can be defined on $A$ containing the ordered pair $(1,2)$ & $(2,1)$ is
Consider set $A = \{1,2,3\}$ . Number of symmetric relations that can be defined on $A$ containing the ordered pair $(1,2)$ & $(2,1)$ is
- A
$18$
- B
$16$
- C
$24$
- D
$32$
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Determine whether each of the following relations are reflexive, symmetric and transitive :
Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3, \ldots, 13,14\}$ defined as $\mathrm{R}=\{(x, y): 3 x-y=0\}$
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Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $R$ is:
Let $A=\{1,2,3,4\}$ and $R$ be a relation on the set $A \times A$ defined by $R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}$. Then the number of elements in $R$ is:
- [JEE MAIN 2023]
Show that the relation $\mathrm{R}$ in the set $\mathrm{Z}$ of integers given by $\mathrm{R} =\{(\mathrm{a}, \mathrm{b}): 2$ divides $\mathrm{a}-\mathrm{b}\}$ is an equivalence relation.
Show that the relation $\mathrm{R}$ in the set $\mathrm{Z}$ of integers given by $\mathrm{R} =\{(\mathrm{a}, \mathrm{b}): 2$ divides $\mathrm{a}-\mathrm{b}\}$ is an equivalence relation.
Show that the relation $R$ in the set $R$ of real numbers, defined as $R =\left\{(a, b): a \leq b^{2}\right\}$ is neither reflexive nor symmetric nor transitive.
Show that the relation $R$ in the set $R$ of real numbers, defined as $R =\left\{(a, b): a \leq b^{2}\right\}$ is neither reflexive nor symmetric nor transitive.