Sets And Relations

Step 1: Reflexive Property.
For the relation $R$ to be reflexive, it must contain the pair $(a%2Ca)$ for every element $a%20%5Cin%20I$ . Here, the relation does not contain $(4%2C4)%2C%20(5%2C5)%2C%20(6%2C6)%2C%20(7%2C7)$ , so $R$ is not reflexive.

Step 2: Symmetric Property.
For the relation to be symmetric, if $(a%2Cb)$ is in the relation, then $(b%2Ca)$ must also be in the relation. Here, $(4%2C5)$ and $(5%2C4)$ are present, and similarly for the other pairs, making $R$ symmetric.

Step 3: Transitive Property.
For the relation to be transitive, if $(a%2Cb)$ and $(b%2Cc)$ are in the relation, then $(a%2Cc)$ must also be in the relation. However, $(4%2C5)$ and $(5%2C4)$ should imply $(4%2C4)$ , but $(4%2C4)$ is not in the relation, so $R$ is not transitive.

Step 4: Antisymmetric Property.
For the relation to be antisymmetric, if $(a%2Cb)$ and $(b%2Ca)$ are in the relation, then $a%20%3D%20b$ . In this case, both $(4%2C5)$ and $(5%2C4)$ are present, but $4%20%5Cneq%205$ and $5%20%5Cneq%204$ , so $R$ is not antisymmetric.

Step 5: Conclusion.
The relation does not have the transitive property, so the correct answer is (1) A, C and D only.

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Sets And Relations

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs