A Relation R on a Set A is a Symmetric Relation iff ……………………….
Question
A relation \( R \) on a set \( A \) is a symmetric relation iff ……………………….
Solution
A relation \( R \) on a set \( A \) is called symmetric if whenever an ordered pair \( (a,b) \) belongs to \( R \), then the ordered pair \( (b,a) \) also belongs to \( R \).
Mathematically,
\[ (a,b)\in R \implies (b,a)\in R \]
for all \( a,b\in A \).
Thus, a relation \( R \) on a set \( A \) is symmetric iff:
\[ (a,b)\in R \Rightarrow (b,a)\in R \]
Hence, the required answer is:
\[ \boxed{(a,b)\in R \Rightarrow (b,a)\in R} \]