JEE MAIN - Mathematics (2018 - 15th April Morning Slot - No. 7)
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 :
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 :
both R1 and R2 are not symmetric.
R1 is not symmetric but it is transitive.
R2 is symmetric but it is not transitive.
both R1 and R2 are transitive.
Explanation
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.
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.
Comments (0)
