Let $N$ be the set of natural numbers greater than $100. $ Define the relation $R$ by : $R = \{(x,y) \in \,N × N :$ the numbers $x$ and $y$ have atleast two common divisors$\}.$ Then $R$ is-
Let $N$ be the set of natural numbers greater than $100. $ Define the relation $R$ by : $R = \{(x,y) \in \,N × N :$ the numbers $x$ and $y$ have atleast two common divisors$\}.$ Then $R$ is-
- A
Reflexive, Symmetric and transitive relation
- B
Symmetric, transitive and NOT Reflexive relation
- C
Reflexive, transitive and NOT Symmetric relation
- D
Reflexive, Symmetric and NOT transitive relation
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- [JEE MAIN 2022]
Let $L$ be the set of all lines in $XY$ plane and $R$ be the relation in $L$ defined as $R =\{\left( L _{1}, L _{2}\right): L _{1} $ is parallel to $L _{2}\} .$ Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y=2 x+4$
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