JEE Main 20241 Feb, Evening shiftMathematicsHardSets, Relations and Functions168× since 2002Consider the relations R1R_1R1 and R2R_2R2 defined as aR1b⇔a2+b2=1a R_1 b \Leftrightarrow a^2+b^2=1aR1b⇔a2+b2=1 for all a,b∈Ra, b \in \mathbf{R}a,b∈R and (a,b)R2(c,d)⇔(a, b) R_2(c, d) \Leftrightarrow(a,b)R2(c,d)⇔ a+d=b+ca+d=b+ca+d=b+c for all (a,b),(c,d)∈N×N(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}(a,b),(c,d)∈N×N. Then :AOption A. R1R_1R1 and R2R_2R2 both are equivalence relationsBOption B. Only R1R_1R1 is an equivalence relationCOption C. Only R2R_2R2 is an equivalence relationDOption D. Neither R1R_1R1 nor R2R_2R2 is an equivalence relationCheckSkip · show solution
