Relations and Types of Relation
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Sets, Relation and Function

116799 The minimum number of elements that must be added to the relation \(R=\{(\mathbf{a}, \mathbf{b}),(\mathbf{b}, \mathbf{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

1 3
2 7
3 4
4 5
Shift-I
Sets, Relation and Function

116800 Let \(R\) be a relation defined an \(N\) as \(a R\) is \(2 a\) \(+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is

1 transitive but not symmetric
2 an equivalence relation
3 symmetric but no transitive
4 not reflexive
Shift-II
Sets, Relation and Function

116802 Among the relations
\(S=\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}-\{0\}, 2+\frac{\mathbf{a}}{\mathbf{b}}>0\right\}\) and \(T=\) \(\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}, \mathbf{a}^2-\mathbf{b}^2 \in Z\right\}\).

1 \(\mathrm{S}\) is transitive but \(\mathrm{T}\) is not transitive
2 both \(\mathrm{S}\) and \(\mathrm{T}\) are symmetric
3 neither \(\mathrm{S}\) nor \(\mathrm{T}\) is transitive
4 \(\mathrm{T}\) is symmetric but \(\mathrm{S}\) is not symmetric
Shift-II
Sets, Relation and Function

116803 Let \(R\) be the relation on the set \(R\) of all real
Numbers defined by setting aRb iff \(|a-b| \leq \frac{1}{2}\)
Then \(R\) is

1 Reflexive and symmetric but not transitive
2 Symmetric and transitive but not reflexive
3 Reflexive and transitive but not symmetric
4 Transitive but neither reflexive nor symmetric
AMU-2021
Sets, Relation and Function

116804 Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the number of ordered pairs which when added to \(R\) make it an equivalence relation is

1 5
2 6
3 7
4 none of these.
AMU-2008
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Sets, Relation and Function

116799 The minimum number of elements that must be added to the relation \(R=\{(\mathbf{a}, \mathbf{b}),(\mathbf{b}, \mathbf{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

1 3
2 7
3 4
4 5
Shift-I
Sets, Relation and Function

116800 Let \(R\) be a relation defined an \(N\) as \(a R\) is \(2 a\) \(+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is

1 transitive but not symmetric
2 an equivalence relation
3 symmetric but no transitive
4 not reflexive
Shift-II
Sets, Relation and Function

116802 Among the relations
\(S=\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}-\{0\}, 2+\frac{\mathbf{a}}{\mathbf{b}}>0\right\}\) and \(T=\) \(\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}, \mathbf{a}^2-\mathbf{b}^2 \in Z\right\}\).

1 \(\mathrm{S}\) is transitive but \(\mathrm{T}\) is not transitive
2 both \(\mathrm{S}\) and \(\mathrm{T}\) are symmetric
3 neither \(\mathrm{S}\) nor \(\mathrm{T}\) is transitive
4 \(\mathrm{T}\) is symmetric but \(\mathrm{S}\) is not symmetric
Shift-II
Sets, Relation and Function

116803 Let \(R\) be the relation on the set \(R\) of all real
Numbers defined by setting aRb iff \(|a-b| \leq \frac{1}{2}\)
Then \(R\) is

1 Reflexive and symmetric but not transitive
2 Symmetric and transitive but not reflexive
3 Reflexive and transitive but not symmetric
4 Transitive but neither reflexive nor symmetric
AMU-2021
Sets, Relation and Function

116804 Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the number of ordered pairs which when added to \(R\) make it an equivalence relation is

1 5
2 6
3 7
4 none of these.
AMU-2008
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Sets, Relation and Function

116799 The minimum number of elements that must be added to the relation \(R=\{(\mathbf{a}, \mathbf{b}),(\mathbf{b}, \mathbf{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

1 3
2 7
3 4
4 5
Shift-I
Sets, Relation and Function

116800 Let \(R\) be a relation defined an \(N\) as \(a R\) is \(2 a\) \(+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is

1 transitive but not symmetric
2 an equivalence relation
3 symmetric but no transitive
4 not reflexive
Shift-II
Sets, Relation and Function

116802 Among the relations
\(S=\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}-\{0\}, 2+\frac{\mathbf{a}}{\mathbf{b}}>0\right\}\) and \(T=\) \(\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}, \mathbf{a}^2-\mathbf{b}^2 \in Z\right\}\).

1 \(\mathrm{S}\) is transitive but \(\mathrm{T}\) is not transitive
2 both \(\mathrm{S}\) and \(\mathrm{T}\) are symmetric
3 neither \(\mathrm{S}\) nor \(\mathrm{T}\) is transitive
4 \(\mathrm{T}\) is symmetric but \(\mathrm{S}\) is not symmetric
Shift-II
Sets, Relation and Function

116803 Let \(R\) be the relation on the set \(R\) of all real
Numbers defined by setting aRb iff \(|a-b| \leq \frac{1}{2}\)
Then \(R\) is

1 Reflexive and symmetric but not transitive
2 Symmetric and transitive but not reflexive
3 Reflexive and transitive but not symmetric
4 Transitive but neither reflexive nor symmetric
AMU-2021
Sets, Relation and Function

116804 Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the number of ordered pairs which when added to \(R\) make it an equivalence relation is

1 5
2 6
3 7
4 none of these.
AMU-2008
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Sets, Relation and Function

116799 The minimum number of elements that must be added to the relation \(R=\{(\mathbf{a}, \mathbf{b}),(\mathbf{b}, \mathbf{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

1 3
2 7
3 4
4 5
Shift-I
Sets, Relation and Function

116800 Let \(R\) be a relation defined an \(N\) as \(a R\) is \(2 a\) \(+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is

1 transitive but not symmetric
2 an equivalence relation
3 symmetric but no transitive
4 not reflexive
Shift-II
Sets, Relation and Function

116802 Among the relations
\(S=\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}-\{0\}, 2+\frac{\mathbf{a}}{\mathbf{b}}>0\right\}\) and \(T=\) \(\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}, \mathbf{a}^2-\mathbf{b}^2 \in Z\right\}\).

1 \(\mathrm{S}\) is transitive but \(\mathrm{T}\) is not transitive
2 both \(\mathrm{S}\) and \(\mathrm{T}\) are symmetric
3 neither \(\mathrm{S}\) nor \(\mathrm{T}\) is transitive
4 \(\mathrm{T}\) is symmetric but \(\mathrm{S}\) is not symmetric
Shift-II
Sets, Relation and Function

116803 Let \(R\) be the relation on the set \(R\) of all real
Numbers defined by setting aRb iff \(|a-b| \leq \frac{1}{2}\)
Then \(R\) is

1 Reflexive and symmetric but not transitive
2 Symmetric and transitive but not reflexive
3 Reflexive and transitive but not symmetric
4 Transitive but neither reflexive nor symmetric
AMU-2021
Sets, Relation and Function

116804 Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the number of ordered pairs which when added to \(R\) make it an equivalence relation is

1 5
2 6
3 7
4 none of these.
AMU-2008
Join With Us for More Updates
Sets, Relation and Function

116799 The minimum number of elements that must be added to the relation \(R=\{(\mathbf{a}, \mathbf{b}),(\mathbf{b}, \mathbf{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

1 3
2 7
3 4
4 5
Shift-I
Sets, Relation and Function

116800 Let \(R\) be a relation defined an \(N\) as \(a R\) is \(2 a\) \(+3 b\) is a multiple of \(5, a, b \in N\). Then \(R\) is

1 transitive but not symmetric
2 an equivalence relation
3 symmetric but no transitive
4 not reflexive
Shift-II
Sets, Relation and Function

116802 Among the relations
\(S=\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}-\{0\}, 2+\frac{\mathbf{a}}{\mathbf{b}}>0\right\}\) and \(T=\) \(\left\{(\mathbf{a}, \mathbf{b}): \mathbf{a}, \mathbf{b} \in \mathbf{R}, \mathbf{a}^2-\mathbf{b}^2 \in Z\right\}\).

1 \(\mathrm{S}\) is transitive but \(\mathrm{T}\) is not transitive
2 both \(\mathrm{S}\) and \(\mathrm{T}\) are symmetric
3 neither \(\mathrm{S}\) nor \(\mathrm{T}\) is transitive
4 \(\mathrm{T}\) is symmetric but \(\mathrm{S}\) is not symmetric
Shift-II
Sets, Relation and Function

116803 Let \(R\) be the relation on the set \(R\) of all real
Numbers defined by setting aRb iff \(|a-b| \leq \frac{1}{2}\)
Then \(R\) is

1 Reflexive and symmetric but not transitive
2 Symmetric and transitive but not reflexive
3 Reflexive and transitive but not symmetric
4 Transitive but neither reflexive nor symmetric
AMU-2021
Sets, Relation and Function

116804 Given the relation \(R=\{(1,2),(2,3)\}\) on the set \(A=\{1,2,3\}\), the number of ordered pairs which when added to \(R\) make it an equivalence relation is

1 5
2 6
3 7
4 none of these.
AMU-2008