Maths · Relations, type of relations, equivalence relations
Let and \{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3) then the relation and is
Let \( A=\{1,2,3\} \) and \( R= \) \{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3) then the relation \( R \) and \( A \) is
- A. reflexive
- B. symmetric
- C. transitive
- D. equivalence
Step-by-step solution
The relation R is reflexive because it contains (1,1), (2,2), and (3,3) for all elements of A. It is not symmetric because (2,1) is present but (1,2) is missing. It is not transitive because (2,1) and (1,3) are present but (2,3) is missing. Thus, only reflexivity holds.
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