Relations and Types of Relation
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Sets, Relation and Function

116824 Let \(R\) be the relation on the set \(R\), of all real numbers defined by aRb if \(f(x)=|a-b| \leq 1\). Then, \(R\) is

1 reflexive and symmetric
2 symmetric only
3 transitive only
4 anti-symmetric only
BCECE-2012
Sets, Relation and Function

116825 On set \(A=\{1,2,3\}\), relations \(R\) and \(S\) are given by
\(\mathbf{R}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1})\},\)
\(\mathrm{S}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}\).
Then,

1 \(\mathrm{R} \cup \mathrm{S}\) is an equivalence relation
2 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and transitive but not symmetric
3 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and symmetric but not transitive
4 \(\mathrm{R} \cup \mathrm{S}\) is symmetric and transitive but no reflexive
WB JEE-2017
Sets, Relation and Function

116828 Let a relation \(R\) be defined on set of all real numbers by \(\mathbf{R} \mathbf{b}\) if and only if \(1+\mathbf{a b}>\mathbf{0}\). Then, \(R\) is

1 reflexive, transitive but not symmetric
2 reflexive, symmetric but not transitive
3 Symmetric, transitive but not reflexive
4 an equivalence relation
UPSEE-2009
Sets, Relation and Function

116830 An integer \(m\) is said to be related to another integer \(n\), if \(m\) is a multiple of \(n\). Then, the relation is

1 reflexive and symmetric
2 reflexive and transitive
3 symmetric and transitive
4 an equivalence relation
UPSEE-2012
Sets, Relation and Function

116831 The relation \(R\) in \(R\) defined by \(R=\{(a, b): a \leq\) \(\mathbf{b}^3\) ), is

1 reflexive
2 symmetric
3 transitive
4 None of these
UPSEE-2014
NEET DIGITAL LIBRARY
Sets, Relation and Function

116824 Let \(R\) be the relation on the set \(R\), of all real numbers defined by aRb if \(f(x)=|a-b| \leq 1\). Then, \(R\) is

1 reflexive and symmetric
2 symmetric only
3 transitive only
4 anti-symmetric only
BCECE-2012
Sets, Relation and Function

116825 On set \(A=\{1,2,3\}\), relations \(R\) and \(S\) are given by
\(\mathbf{R}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1})\},\)
\(\mathrm{S}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}\).
Then,

1 \(\mathrm{R} \cup \mathrm{S}\) is an equivalence relation
2 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and transitive but not symmetric
3 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and symmetric but not transitive
4 \(\mathrm{R} \cup \mathrm{S}\) is symmetric and transitive but no reflexive
WB JEE-2017
Sets, Relation and Function

116828 Let a relation \(R\) be defined on set of all real numbers by \(\mathbf{R} \mathbf{b}\) if and only if \(1+\mathbf{a b}>\mathbf{0}\). Then, \(R\) is

1 reflexive, transitive but not symmetric
2 reflexive, symmetric but not transitive
3 Symmetric, transitive but not reflexive
4 an equivalence relation
UPSEE-2009
Sets, Relation and Function

116830 An integer \(m\) is said to be related to another integer \(n\), if \(m\) is a multiple of \(n\). Then, the relation is

1 reflexive and symmetric
2 reflexive and transitive
3 symmetric and transitive
4 an equivalence relation
UPSEE-2012
Sets, Relation and Function

116831 The relation \(R\) in \(R\) defined by \(R=\{(a, b): a \leq\) \(\mathbf{b}^3\) ), is

1 reflexive
2 symmetric
3 transitive
4 None of these
UPSEE-2014
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Sets, Relation and Function

116824 Let \(R\) be the relation on the set \(R\), of all real numbers defined by aRb if \(f(x)=|a-b| \leq 1\). Then, \(R\) is

1 reflexive and symmetric
2 symmetric only
3 transitive only
4 anti-symmetric only
BCECE-2012
Sets, Relation and Function

116825 On set \(A=\{1,2,3\}\), relations \(R\) and \(S\) are given by
\(\mathbf{R}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1})\},\)
\(\mathrm{S}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}\).
Then,

1 \(\mathrm{R} \cup \mathrm{S}\) is an equivalence relation
2 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and transitive but not symmetric
3 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and symmetric but not transitive
4 \(\mathrm{R} \cup \mathrm{S}\) is symmetric and transitive but no reflexive
WB JEE-2017
Sets, Relation and Function

116828 Let a relation \(R\) be defined on set of all real numbers by \(\mathbf{R} \mathbf{b}\) if and only if \(1+\mathbf{a b}>\mathbf{0}\). Then, \(R\) is

1 reflexive, transitive but not symmetric
2 reflexive, symmetric but not transitive
3 Symmetric, transitive but not reflexive
4 an equivalence relation
UPSEE-2009
Sets, Relation and Function

116830 An integer \(m\) is said to be related to another integer \(n\), if \(m\) is a multiple of \(n\). Then, the relation is

1 reflexive and symmetric
2 reflexive and transitive
3 symmetric and transitive
4 an equivalence relation
UPSEE-2012
Sets, Relation and Function

116831 The relation \(R\) in \(R\) defined by \(R=\{(a, b): a \leq\) \(\mathbf{b}^3\) ), is

1 reflexive
2 symmetric
3 transitive
4 None of these
UPSEE-2014
For More Updates join with Us
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Sets, Relation and Function

116824 Let \(R\) be the relation on the set \(R\), of all real numbers defined by aRb if \(f(x)=|a-b| \leq 1\). Then, \(R\) is

1 reflexive and symmetric
2 symmetric only
3 transitive only
4 anti-symmetric only
BCECE-2012
Sets, Relation and Function

116825 On set \(A=\{1,2,3\}\), relations \(R\) and \(S\) are given by
\(\mathbf{R}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1})\},\)
\(\mathrm{S}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}\).
Then,

1 \(\mathrm{R} \cup \mathrm{S}\) is an equivalence relation
2 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and transitive but not symmetric
3 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and symmetric but not transitive
4 \(\mathrm{R} \cup \mathrm{S}\) is symmetric and transitive but no reflexive
WB JEE-2017
Sets, Relation and Function

116828 Let a relation \(R\) be defined on set of all real numbers by \(\mathbf{R} \mathbf{b}\) if and only if \(1+\mathbf{a b}>\mathbf{0}\). Then, \(R\) is

1 reflexive, transitive but not symmetric
2 reflexive, symmetric but not transitive
3 Symmetric, transitive but not reflexive
4 an equivalence relation
UPSEE-2009
Sets, Relation and Function

116830 An integer \(m\) is said to be related to another integer \(n\), if \(m\) is a multiple of \(n\). Then, the relation is

1 reflexive and symmetric
2 reflexive and transitive
3 symmetric and transitive
4 an equivalence relation
UPSEE-2012
Sets, Relation and Function

116831 The relation \(R\) in \(R\) defined by \(R=\{(a, b): a \leq\) \(\mathbf{b}^3\) ), is

1 reflexive
2 symmetric
3 transitive
4 None of these
UPSEE-2014
NEET DIGITAL LIBRARY
Sets, Relation and Function

116824 Let \(R\) be the relation on the set \(R\), of all real numbers defined by aRb if \(f(x)=|a-b| \leq 1\). Then, \(R\) is

1 reflexive and symmetric
2 symmetric only
3 transitive only
4 anti-symmetric only
BCECE-2012
Sets, Relation and Function

116825 On set \(A=\{1,2,3\}\), relations \(R\) and \(S\) are given by
\(\mathbf{R}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{2}),(\mathbf{2}, \mathbf{1})\},\)
\(\mathrm{S}=\{(\mathbf{1}, \mathbf{1}),(\mathbf{2}, \mathbf{2}),(\mathbf{3}, \mathbf{3}),(\mathbf{1}, \mathbf{3}),(\mathbf{3}, \mathbf{1})\}\).
Then,

1 \(\mathrm{R} \cup \mathrm{S}\) is an equivalence relation
2 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and transitive but not symmetric
3 \(\mathrm{R} \cup \mathrm{S}\) is reflexive and symmetric but not transitive
4 \(\mathrm{R} \cup \mathrm{S}\) is symmetric and transitive but no reflexive
WB JEE-2017
Sets, Relation and Function

116828 Let a relation \(R\) be defined on set of all real numbers by \(\mathbf{R} \mathbf{b}\) if and only if \(1+\mathbf{a b}>\mathbf{0}\). Then, \(R\) is

1 reflexive, transitive but not symmetric
2 reflexive, symmetric but not transitive
3 Symmetric, transitive but not reflexive
4 an equivalence relation
UPSEE-2009
Sets, Relation and Function

116830 An integer \(m\) is said to be related to another integer \(n\), if \(m\) is a multiple of \(n\). Then, the relation is

1 reflexive and symmetric
2 reflexive and transitive
3 symmetric and transitive
4 an equivalence relation
UPSEE-2012
Sets, Relation and Function

116831 The relation \(R\) in \(R\) defined by \(R=\{(a, b): a \leq\) \(\mathbf{b}^3\) ), is

1 reflexive
2 symmetric
3 transitive
4 None of these
UPSEE-2014