Consider the following two binary relations on the set A = a, b, c : R1 = (c, a), (b, b), …

Question

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 :

Accepted Answer

Here both R1 and R2 are symmetric as for any (x, y) $$ \in $$ R1, we have (y, x) $$ \in $$ R1 and similarly for any (x, y) $$ \in $$ R2,  we have (y, x) $$ \in $$ R2

In R1, (b, c) $$ \in $$ R1, (c, a) $$ \in $$ R1 but (b,a) $$ \notin $$ R1

Similarly in R2, (b, a) $$ \in $$ R2, (a, c) $$ \in $$ R2 but (b, c) $$ \notin $$ R2

$$ \therefore $$ R1 and R2 are not transitive.

Solutions · 1