Question

Let H be the set of all houses in a village where each house is faced in one of the directions, East, West, North, South.
Let $R=\left\{\right(x,y\left)|\right(x,y)\in H\times H\text{and x, y are faced in same direction}\}$. Then the relation 'R' is -

• A. Non symmetric
• B. Only reflexive and symmetric
• C. Non reflexive
• D. An equivalence relation

Answer 1

The correct option is D An equivalence relation

$(x,x)\in R$. Thus, R is reflexive

$(x,y)\in R\Rightarrow (y,x)\in R$. Thus, R is symmetric

$(x,y)\in R,(y,z)\in R\Rightarrow (x,z)\in R$. Thus, R is transitive.

So, 'R' is the equivalence relation.