Question

If \( R \) be a relation defined as \( a \, R \, b \) iff \( |a - b|>0 \), \( a, b \in \mathbb{R} \), then \( R \) is :

• A. reflexive
• B. symmetric
• C. transitive
• D. symmetric and transitive

Hint:

To check if a relation is symmetric, verify if \( a \, R \, b \implies b \, R \, a \).

Answer 1

The Correct Option is B

For a relation to be reflexive, it must satisfy \( a \, R \, a \), which is not the case here, because \( |a - a| = 0 \), and the condition is \( |a - b|>0 \). For a relation to be symmetric, if \( a \, R \, b \), then \( b \, R \, a \). Since \( |a - b| = |b - a| \), the relation is symmetric.
Thus, the correct answer is (B).