JEE Main 2018 — Sets And Relations Question with Solution
From: JEE Main 2018 (Online) 15th April Morning Slot
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 :
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 :
Choose an option
Show full solutionCorrect option: C
Correct answer
CR2 is symmetric but it is not transitive.
Step-by-step explanation
Here both R1 and R2 are symmetric as for any (x, y) R1, we have (y, x) R1 and similarly for any (x, y) R2, we have (y, x) R2
In R1, (b, c) R1, (c, a) R1 but (b,a) R1
Similarly in R2, (b, a) R2, (a, c) R2 but (b, c) R2
R1 and R2 are not transitive.
In R1, (b, c) R1, (c, a) R1 but (b,a) R1
Similarly in R2, (b, a) R2, (a, c) R2 but (b, c) R2
R1 and R2 are not transitive.
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