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Answer the following.
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation…
If a relation $R$ on the set $\{a, b, c\}$ defined by $R = \{(b, b)\}$, then classify the relation. (Understanding)
Answer
Answer
Official answer keyThe relation is: reflexive: no; symmetric: yes; transitive: yes; equivalence: no; antisymmetric: yes
The relation is symmetric and transitive but not reflexive.
Not reflexive: $(a,a), (c,c) \notin R$. Symmetric: $(b,b)$ is its own reverse. Transitive: $(b,b),(b,b) \Rightarrow (b,b) \in R$.