JEE Mains · Maths · STD 12 - 1. relation and function
Consider the following two binary relations on the set \(A= \{a, b, c\}\) : \(R_1 = \{(c, a) (b, b) , (a, c), (c,c), (b, c), (a, a)\}\) and \(R_2 = \{(a, b), (b, a), (c, c), (c,a), (a, a), (b, b), (a, c)\}.\) Then
- A \(R_2\) is symmetric but it is not transitive
- B Both \(R_1\) and \(R_2\) are transitive
- C Both \(R_1\) and \(R_2\) are not symmetric
- D \(R_1\) is not symmetric but it is transitive
Answer & Solution
Correct Answer
(A) \(R_2\) is symmetric but it is not transitive
Step-by-step Solution
Detailed explanation
both \({R_1}\) and \({R_2}\) are symmetric as For any \(\left( {x,y} \right) \in {R_1}\), we have \(\left( {y,x} \right) \in {R_1}\) and similarly for \({R_2}\) Now, for \({R_2},\left( {b,a} \right) \in {R_2},\left( {a,c} \right) \in {R_2}\) but…
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