Verified Solution • 2025–26 Session moderate

QJEEM18Macd91: JEE Main 2018 Mathematics - Class 11 JEEM18Macd91 Solution: Consider the following two binary relations on the set A = {a,…

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 :

Multiple Choice Options

  • A both R1 and R2 are not symmetric.
  • B R1 is not symmetric but it is transitive.
  • C R2 is symmetric but it is not transitive.
  • D both R1 and R2 are transitive.

Step-by-Step Verified Solution

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.

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