Consider the following two binary relations on the set A = a ,   b ,   c   :   R 1 = c ,…

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 :
  1. R2 is symmetric but it is not transitive
  2. both R1 and R2 are not symmetric
  3. both R1 and R2 are transitive
  4. R1 is not symmetric but it is transitive

Solution

Since, (b, c)∈R1 but (c, b)∉R1 

Hence, R1 is not symmetric.

In R1 : b, c∈R1 and c, a∈R1 but b, a∉R1

So, R1 is not transitive.

R2 is symmetric.

In R2 : b, a∈R2 and a, c∈R1 but b, c∉R2

So, R2 is not transitive.

Asked in: JEE Main 2018 (15 Apr)

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