Relations and Types of Relation
Sets, Relation and Function

116815 Let \(R\) be the set of real numbers and let \(G \subseteq R^2\) be a relation defined by \(\mathbf{G}=\{[(\mathbf{a}, \mathbf{b}),(\mathbf{c}, \mathbf{d})][\mathbf{b}-\) \(\mathbf{a}=\mathbf{d}-\mathbf{c}]\}\) then \(\mathbf{G}\) is

1 reflexive only
2 symmetric only
3 transitive only
4 an equivalence relation
Sets, Relation and Function

116823 The relations \(R\) defined in the set \(\{1,2,3,4,5\), \(6\}\) as \(R=\{(a, b): b=a+1\}\) is

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

116817 Let \(A=\{1,3,4,6,9)\) and \(B=\{2,4,5,8,10\}\). Let \(R\) be a relation defined on \(A \times B\) such that \(R=\) \(\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right): a_1 \leq b_2\right.\) and \(\left.b_1 \leq a_2\right\}\).
Then the number of elements in the set \(R\) is

1 26
2 160
3 180
4 52
Sets, Relation and Function

116818 Let \(R\) be the relation in the set \(\{x: x \in N, x \leq 4\}\) given by \(R=\{(1,1),(2,2),(3,3)\}\) 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 An equivalence relation.
Sets, Relation and Function

116815 Let \(R\) be the set of real numbers and let \(G \subseteq R^2\) be a relation defined by \(\mathbf{G}=\{[(\mathbf{a}, \mathbf{b}),(\mathbf{c}, \mathbf{d})][\mathbf{b}-\) \(\mathbf{a}=\mathbf{d}-\mathbf{c}]\}\) then \(\mathbf{G}\) is

1 reflexive only
2 symmetric only
3 transitive only
4 an equivalence relation
Sets, Relation and Function

116823 The relations \(R\) defined in the set \(\{1,2,3,4,5\), \(6\}\) as \(R=\{(a, b): b=a+1\}\) is

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

116817 Let \(A=\{1,3,4,6,9)\) and \(B=\{2,4,5,8,10\}\). Let \(R\) be a relation defined on \(A \times B\) such that \(R=\) \(\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right): a_1 \leq b_2\right.\) and \(\left.b_1 \leq a_2\right\}\).
Then the number of elements in the set \(R\) is

1 26
2 160
3 180
4 52
Sets, Relation and Function

116818 Let \(R\) be the relation in the set \(\{x: x \in N, x \leq 4\}\) given by \(R=\{(1,1),(2,2),(3,3)\}\) 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 An equivalence relation.
Sets, Relation and Function

116815 Let \(R\) be the set of real numbers and let \(G \subseteq R^2\) be a relation defined by \(\mathbf{G}=\{[(\mathbf{a}, \mathbf{b}),(\mathbf{c}, \mathbf{d})][\mathbf{b}-\) \(\mathbf{a}=\mathbf{d}-\mathbf{c}]\}\) then \(\mathbf{G}\) is

1 reflexive only
2 symmetric only
3 transitive only
4 an equivalence relation
Sets, Relation and Function

116823 The relations \(R\) defined in the set \(\{1,2,3,4,5\), \(6\}\) as \(R=\{(a, b): b=a+1\}\) is

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

116817 Let \(A=\{1,3,4,6,9)\) and \(B=\{2,4,5,8,10\}\). Let \(R\) be a relation defined on \(A \times B\) such that \(R=\) \(\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right): a_1 \leq b_2\right.\) and \(\left.b_1 \leq a_2\right\}\).
Then the number of elements in the set \(R\) is

1 26
2 160
3 180
4 52
Sets, Relation and Function

116818 Let \(R\) be the relation in the set \(\{x: x \in N, x \leq 4\}\) given by \(R=\{(1,1),(2,2),(3,3)\}\) 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 An equivalence relation.
Sets, Relation and Function

116815 Let \(R\) be the set of real numbers and let \(G \subseteq R^2\) be a relation defined by \(\mathbf{G}=\{[(\mathbf{a}, \mathbf{b}),(\mathbf{c}, \mathbf{d})][\mathbf{b}-\) \(\mathbf{a}=\mathbf{d}-\mathbf{c}]\}\) then \(\mathbf{G}\) is

1 reflexive only
2 symmetric only
3 transitive only
4 an equivalence relation
Sets, Relation and Function

116823 The relations \(R\) defined in the set \(\{1,2,3,4,5\), \(6\}\) as \(R=\{(a, b): b=a+1\}\) is

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

116817 Let \(A=\{1,3,4,6,9)\) and \(B=\{2,4,5,8,10\}\). Let \(R\) be a relation defined on \(A \times B\) such that \(R=\) \(\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right): a_1 \leq b_2\right.\) and \(\left.b_1 \leq a_2\right\}\).
Then the number of elements in the set \(R\) is

1 26
2 160
3 180
4 52
Sets, Relation and Function

116818 Let \(R\) be the relation in the set \(\{x: x \in N, x \leq 4\}\) given by \(R=\{(1,1),(2,2),(3,3)\}\) 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 An equivalence relation.