Final answer:
A relation 'r' is described as circular if 'arb' and 'brc' imply an equivalence relation. To be circular, 'r' must satisfy reflexivity, symmetry, and transitivity. Without more context about 'r', it cannot be determined whether 'r' is circular.
Step-by-step explanation:
The original question appears to ask about the properties of a particular type of relation, but without more context, it's unclear what the specific properties of 'r' are meant to be. The student asks if a relation 'r' would be circular, given that 'arb' and 'brc' imply that 'r' is an equivalence relation. However, to be an equivalence relation, 'r' must satisfy three conditions: reflexivity, symmetry, and transitivity.
As per the typical definition in mathematics, if 'arb' and 'brc' are true, to be circular and thus an equivalence relation, it must also be true that 'arc' (transitivity), 'ara' (reflexivity), and if we know 'arb', then 'bra' must also be true (symmetry). If all these conditions are met, 'r' is an equivalence relation and could be circular as described. Unfortunately, without specific properties or additional information about 'r', we cannot conclusively determine whether 'r' is circular based on the description given.