Let $R$ be a relation defined on $N \times N$ by $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(b + d)$ is incorrect,the correct relation is $(a, b) R(c, d) \Leftrightarrow ad = bc$. Given the relation $(a, b) R(c, d) \Leftrightarrow a(b + d) = c(a + d)$ is not standard,let us analyze the relation $(a, b) R(c, d) \Leftrightarrow ad = bc$. Then $R$ is:
- Areflexive,symmetric
- Bsymmetric,transitive
- Ctransitive only
- Dequivalence
Explore More
Similar Questions
Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b| \text{ is even}\}$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $\{2,4\}$ are related to each other,but no element of $\{1,3,5\}$ is related to any element of $\{2,4\}$.
Medium
View SolutionThe relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then $R^{-1}$ is given by
Medium
View SolutionIn order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation,it is sufficient,if $R$
Easy
View SolutionFor the real numbers $x$ and $y$, we define the relation $p$ as $x p y$ if $x-y+\sqrt{2}$ is an irrational number. Then the relation $p$ is
Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \perp \beta$,where $\alpha, \beta \in L$. Then $R$ is
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo