Relations and Types of Relation
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Sets, Relation and Function

116819 Relation \(\mathrm{S}=\{(1,2),(2,1),(2,3)\}\) is defined on the set \(\{1,2,3\}\) is

1 not transitive
2 symmetric
3 reflexive
4 equivalence
GUJCET-2017
Sets, Relation and Function

116820 Relation \(\mathbf{R}\) in the set \(\left(\pi, \pi^2, \pi^3\right)\) defined by \(\mathbf{R}=\) \(\left\{(\pi, \pi),\left(\pi^2, \pi^2\right),\left(\pi^3, \pi^3\right),\left(\pi, \pi^2\right),\left(\pi^2, \pi^3\right)\right\}\) is :

1 Reflexive but neither symmetric nor transitive
2 Symmetric but neither reflexive nor transitive
3 Transitive but neither reflexive nor symmetric
4 Only symmetric and transitive
GUJCET-2023
Sets, Relation and Function

116821 When \(R\) is the set of all real numbers,
\(\left\{x \in R: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\sqrt{12-x-x^2}}{2 x+9}\right\}=\)

1 \((-4,1] \cup\{3\}\)
2 \([-4,1]\)
3 \([-4,1] \cup\{3\}\)
4 \(\phi\), the empty set
Shift-II
Sets, Relation and Function

116822 Let \(A=\{1,2,3,4,5,6,7\}\). Then the relation \(R\) \(=\{(\mathbf{x}, \mathbf{y}) \in \mathbf{A} \times \mathbf{A}: \mathbf{x}+\mathbf{y}=7\}\) is

1 transitive but neither symmetric nor reflexive
2 reflexive but neither symmetric nor transitive
3 an equivalence relation
4 symmetric but neither reflexive nor transitive
Shift-II
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Sets, Relation and Function

116819 Relation \(\mathrm{S}=\{(1,2),(2,1),(2,3)\}\) is defined on the set \(\{1,2,3\}\) is

1 not transitive
2 symmetric
3 reflexive
4 equivalence
GUJCET-2017
Sets, Relation and Function

116820 Relation \(\mathbf{R}\) in the set \(\left(\pi, \pi^2, \pi^3\right)\) defined by \(\mathbf{R}=\) \(\left\{(\pi, \pi),\left(\pi^2, \pi^2\right),\left(\pi^3, \pi^3\right),\left(\pi, \pi^2\right),\left(\pi^2, \pi^3\right)\right\}\) is :

1 Reflexive but neither symmetric nor transitive
2 Symmetric but neither reflexive nor transitive
3 Transitive but neither reflexive nor symmetric
4 Only symmetric and transitive
GUJCET-2023
Sets, Relation and Function

116821 When \(R\) is the set of all real numbers,
\(\left\{x \in R: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\sqrt{12-x-x^2}}{2 x+9}\right\}=\)

1 \((-4,1] \cup\{3\}\)
2 \([-4,1]\)
3 \([-4,1] \cup\{3\}\)
4 \(\phi\), the empty set
Shift-II
Sets, Relation and Function

116822 Let \(A=\{1,2,3,4,5,6,7\}\). Then the relation \(R\) \(=\{(\mathbf{x}, \mathbf{y}) \in \mathbf{A} \times \mathbf{A}: \mathbf{x}+\mathbf{y}=7\}\) is

1 transitive but neither symmetric nor reflexive
2 reflexive but neither symmetric nor transitive
3 an equivalence relation
4 symmetric but neither reflexive nor transitive
Shift-II
NEET DIGITAL LIBRARY
Sets, Relation and Function

116819 Relation \(\mathrm{S}=\{(1,2),(2,1),(2,3)\}\) is defined on the set \(\{1,2,3\}\) is

1 not transitive
2 symmetric
3 reflexive
4 equivalence
GUJCET-2017
Sets, Relation and Function

116820 Relation \(\mathbf{R}\) in the set \(\left(\pi, \pi^2, \pi^3\right)\) defined by \(\mathbf{R}=\) \(\left\{(\pi, \pi),\left(\pi^2, \pi^2\right),\left(\pi^3, \pi^3\right),\left(\pi, \pi^2\right),\left(\pi^2, \pi^3\right)\right\}\) is :

1 Reflexive but neither symmetric nor transitive
2 Symmetric but neither reflexive nor transitive
3 Transitive but neither reflexive nor symmetric
4 Only symmetric and transitive
GUJCET-2023
Sets, Relation and Function

116821 When \(R\) is the set of all real numbers,
\(\left\{x \in R: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\sqrt{12-x-x^2}}{2 x+9}\right\}=\)

1 \((-4,1] \cup\{3\}\)
2 \([-4,1]\)
3 \([-4,1] \cup\{3\}\)
4 \(\phi\), the empty set
Shift-II
Sets, Relation and Function

116822 Let \(A=\{1,2,3,4,5,6,7\}\). Then the relation \(R\) \(=\{(\mathbf{x}, \mathbf{y}) \in \mathbf{A} \times \mathbf{A}: \mathbf{x}+\mathbf{y}=7\}\) is

1 transitive but neither symmetric nor reflexive
2 reflexive but neither symmetric nor transitive
3 an equivalence relation
4 symmetric but neither reflexive nor transitive
Shift-II
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Sets, Relation and Function

116819 Relation \(\mathrm{S}=\{(1,2),(2,1),(2,3)\}\) is defined on the set \(\{1,2,3\}\) is

1 not transitive
2 symmetric
3 reflexive
4 equivalence
GUJCET-2017
Sets, Relation and Function

116820 Relation \(\mathbf{R}\) in the set \(\left(\pi, \pi^2, \pi^3\right)\) defined by \(\mathbf{R}=\) \(\left\{(\pi, \pi),\left(\pi^2, \pi^2\right),\left(\pi^3, \pi^3\right),\left(\pi, \pi^2\right),\left(\pi^2, \pi^3\right)\right\}\) is :

1 Reflexive but neither symmetric nor transitive
2 Symmetric but neither reflexive nor transitive
3 Transitive but neither reflexive nor symmetric
4 Only symmetric and transitive
GUJCET-2023
Sets, Relation and Function

116821 When \(R\) is the set of all real numbers,
\(\left\{x \in R: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\sqrt{12-x-x^2}}{2 x+9}\right\}=\)

1 \((-4,1] \cup\{3\}\)
2 \([-4,1]\)
3 \([-4,1] \cup\{3\}\)
4 \(\phi\), the empty set
Shift-II
Sets, Relation and Function

116822 Let \(A=\{1,2,3,4,5,6,7\}\). Then the relation \(R\) \(=\{(\mathbf{x}, \mathbf{y}) \in \mathbf{A} \times \mathbf{A}: \mathbf{x}+\mathbf{y}=7\}\) is

1 transitive but neither symmetric nor reflexive
2 reflexive but neither symmetric nor transitive
3 an equivalence relation
4 symmetric but neither reflexive nor transitive
Shift-II
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