Types Of Relations

Step 1: Understand the properties of the relation.
The relation is reflexive because . It is symmetric because if , then .
Step 2: Conclusion.
The relation is reflexive and symmetric, but not transitive. Final Answer:

Step 1: All elements are present, so the relation is reflexive.
Step 2: If and are in , then is also in , hence transitive.
Step 3: Relation is not symmetric as is not present.

Step 1: If , then .
Step 2: Hence relation is symmetric.

If (x,y)∈ρ, then x²+y²=1⟹ y²+x²=1. Hence (y,x)∈ρ, so the relation is symmetric.