Browse Questions

True or False: The relation R on the set A={1,2,3} defined as R={(1,1),(1,2),(2,1),(3,3)} is reflexive,symmetric and transitive.

Toolbox:
• A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
• A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
• A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
Given $A=\{1,2,3\}$

$R=\{(1,1),(1,2)(2,1),(3,3)\}$

The relation does not contain (2,2)

Therefore R is not reflexive

The given statment that R is reflexive , symmetric and transitive is 'False'

edited Mar 28, 2013 by meena.p