Irrational Numbers

We are given that if and only if is irrational. Step 1: Checking Reflexivity For to be reflexive, must hold for every . Since is irrational, . Thus, is reflexive.
Step 2: Checking Symmetry For symmetry, if , then we must check if holds. Since the sum of an irrational number and a rational number may not always be irrational, is not symmetric.
Step 3: Checking Transitivity For transitivity, if and , then should hold. Adding both equations: Since is irrational, may or may not be irrational. Thus, is not transitive. Final Answer: is reflexive but neither symmetric nor transitive. Thus, the correct option is .