Both R1 and R2 are symmetric as For any (x,y)∈R1, we have (y,x)∈R1 and similarly for R2 Now, for R2,(b,a)∈R2,(a,c)∈R2 but (b,c)∈/R2. Similarly, for R1,(b,c)∈R1,(c,a)∈R1 but (b,a)∈/R1. Therefore, neither R1 nor R2 is transitive.
Consider the following two binary relations on the set A={a,b,c}:R1={(c,a)(b,b),(a,c),(c, c),(b,c),(a,a)} and R2={(a,b),(b,a),(c,c), (c, a), (a, a), (b, b), (a, c). Then
Held on 15 Apr 2018 · Verified 6 Jul 2026.
R2 is symmetric but it is not transitive
Both R1 and R2 are transitive
Both R1 and R2 are not symmetric
R1 is not symmetric but it is transitive
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