Maths · Relations, type of relations, equivalence relations
is a relation in and \notin \mathrm{r}, \) implies (b, a) then is said to be rel
\( \mathrm{R} \) is a relation in \( \mathrm{A} \) and \( (\mathrm{a}, \mathrm{b}) \notin \mathrm{r}, \) implies (b, a) \( \notin \mathrm{R} \) then \( \mathrm{R} \) is said to be relation
- A. symmetric
- B. contradictory
- C. skew symmetric
- D. none of these
Step-by-step solution
The given condition (a,b)∉R ⇒ (b,a)∉R is logically equivalent to (b,a)∈R ⇒ (a,b)∈R, which is the definition of a symmetric relation. Therefore, R is symmetric.
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