Question

I is the symentric line of ∆ABC,Then its set of ordered pairs will be

Answer 1

The relation R on Z×Z is defined by

(x,y)R(u,v)⇔xv=yu for all (x,y),(u,v)∈Z×Z

We observe the following properties of R on Z×Z

Reflexivity: For any (x,y)∈Z×Z

xy=yx

⇒ (x,y)R(x,y)

Thus, (x,y)R(x,y) for all (x,y)∈Z×Z

So, R is a reflexive relation on Z×Z

Symmetry: Let (x,y),(u,v)∈Z×Zsuch that (x,y)R(u,v). Then, (x,y)R(u,v)⇒xv=yu⇒uy=vx⇒(u,v)R(x,y)

Thus, (x,y)R(u,v)⇒(u,v)R(x,y) for all (x,y),(u,v)∈Z×Z

So, R is a symmetric relation on Z

Transitivity: Let (x,y),(u,v),(a,b)∈Z×Z be such that (x,y)R