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# Engineering

Let R_{1} and R_{2} be two relations defined as follows : \mathrm{R}_{1}=\left[(\mathrm{a}, \mathrm{b}) \in \mathrm{R}^{2} ; \mathrm{a}^{2}+\mathrm{b}^{2} \in \mathrm{Q}\right] and  \mathrm{R}_{2}=\left[(\mathrm{a}, \mathrm{b}) \in \mathrm{R}^{2}: \mathrm{a}^{2}+\mathrm{b}^{2} \notin \mathrm{Q}\right]where Q is the set of all rational numbers. Then :  
Option: 1 Neither R_1 nor R_{2} is transitive.
Option: 2 R_{2} is transitive but R_1 is not transitive.  
Option: 3 R_1 is transitive but R_{2} is not transitive.
Option: 4 R_1 and R_{2} are both transitive.

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