116795 Let \(R\) be a relation from the set \(\{1,2\), 3.........,60 to itself such that \(R=\{(\mathbf{a}, \mathbf{b}): \mathbf{b}=\) pq, where \(p, q \geq 3\) are prime numbers \(\}\). Then the number of elements in \(R\) is :

116796 Let \(P(S)\) denote the power set of \(S=\{1,2\), 3....,10 . Define the relation \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left(A \cap B^C\right) \cup\left(B \cap A^C\right)=\phi\) and \(A R_2 B\) if \(A \cup B^C=B \cup A^C, \forall A, B \in P(S)\). Then

116797 Let a relation \(R\) in the set \(N\) of natural numbers be defined as \((x, y) \Leftrightarrow x^2-4 x y+3 y^2=0 \forall x, y \in\) N. The relation \(R\) is

116798 Let \(r\) be a relation from \(R\) (set of real numbers) to \(R\) defined by \(r=\{(a, b) \mid \mathbf{a}, \mathbf{b} \in \mathbf{R}\) and \(\mathbf{a}-\mathbf{b}+\) \(\sqrt{3}\) is an irrational number \(\}\). The relation \(r\) is

116795 Let \(R\) be a relation from the set \(\{1,2\), 3.........,60 to itself such that \(R=\{(\mathbf{a}, \mathbf{b}): \mathbf{b}=\) pq, where \(p, q \geq 3\) are prime numbers \(\}\). Then the number of elements in \(R\) is :

116796 Let \(P(S)\) denote the power set of \(S=\{1,2\), 3....,10 . Define the relation \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left(A \cap B^C\right) \cup\left(B \cap A^C\right)=\phi\) and \(A R_2 B\) if \(A \cup B^C=B \cup A^C, \forall A, B \in P(S)\). Then

116797 Let a relation \(R\) in the set \(N\) of natural numbers be defined as \((x, y) \Leftrightarrow x^2-4 x y+3 y^2=0 \forall x, y \in\) N. The relation \(R\) is

116798 Let \(r\) be a relation from \(R\) (set of real numbers) to \(R\) defined by \(r=\{(a, b) \mid \mathbf{a}, \mathbf{b} \in \mathbf{R}\) and \(\mathbf{a}-\mathbf{b}+\) \(\sqrt{3}\) is an irrational number \(\}\). The relation \(r\) is

116795 Let \(R\) be a relation from the set \(\{1,2\), 3.........,60 to itself such that \(R=\{(\mathbf{a}, \mathbf{b}): \mathbf{b}=\) pq, where \(p, q \geq 3\) are prime numbers \(\}\). Then the number of elements in \(R\) is :

116796 Let \(P(S)\) denote the power set of \(S=\{1,2\), 3....,10 . Define the relation \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left(A \cap B^C\right) \cup\left(B \cap A^C\right)=\phi\) and \(A R_2 B\) if \(A \cup B^C=B \cup A^C, \forall A, B \in P(S)\). Then

116797 Let a relation \(R\) in the set \(N\) of natural numbers be defined as \((x, y) \Leftrightarrow x^2-4 x y+3 y^2=0 \forall x, y \in\) N. The relation \(R\) is

116798 Let \(r\) be a relation from \(R\) (set of real numbers) to \(R\) defined by \(r=\{(a, b) \mid \mathbf{a}, \mathbf{b} \in \mathbf{R}\) and \(\mathbf{a}-\mathbf{b}+\) \(\sqrt{3}\) is an irrational number \(\}\). The relation \(r\) is

116795 Let \(R\) be a relation from the set \(\{1,2\), 3.........,60 to itself such that \(R=\{(\mathbf{a}, \mathbf{b}): \mathbf{b}=\) pq, where \(p, q \geq 3\) are prime numbers \(\}\). Then the number of elements in \(R\) is :

116796 Let \(P(S)\) denote the power set of \(S=\{1,2\), 3....,10 . Define the relation \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left(A \cap B^C\right) \cup\left(B \cap A^C\right)=\phi\) and \(A R_2 B\) if \(A \cup B^C=B \cup A^C, \forall A, B \in P(S)\). Then

116797 Let a relation \(R\) in the set \(N\) of natural numbers be defined as \((x, y) \Leftrightarrow x^2-4 x y+3 y^2=0 \forall x, y \in\) N. The relation \(R\) is

116798 Let \(r\) be a relation from \(R\) (set of real numbers) to \(R\) defined by \(r=\{(a, b) \mid \mathbf{a}, \mathbf{b} \in \mathbf{R}\) and \(\mathbf{a}-\mathbf{b}+\) \(\sqrt{3}\) is an irrational number \(\}\). The relation \(r\) is