urgently need help
Hello, srk619!
State, with reasons, whether the raltion R on $\displaystyle N\times N,$
. . given by $\displaystyle mRn\text{ if }m \geq n$ is an equivalence relation.
Reflexive: .Is $\displaystyle aR\,a$ for all $\displaystyle a?$
. . Since $\displaystyle a \geq\,a$ for all $\displaystyle a$, it is reflexive.
Symmetric: .If $\displaystyle aR\,b$, does $\displaystyle bR\,a ?$
. . If $\displaystyle a \geq b$, then it may or may not be true that: $\displaystyle b \geq a$
. . Hence: $\displaystyle R$ is not symmetric.
Therefore, $\displaystyle R$ is not an equivalence relation.