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Consider the relations \(R_1\) and \(R_2\) defined as \(a{R}_{1}b\Leftrightarrow {a}^{2}+{b}^{2}=1\) for all \(a, b \in …

Q1

Consider the relations \(R_1\) and \(R_2\) defined as \(a{R}_{1}b\Leftrightarrow {a}^{2}+{b}^{2}=1\) for all \(a, b \in R\) and \((a,b){R}_{2}(c,d)\Leftrightarrow\) \(a+d=b+c\) for all \(( a , b ),( c , d ) \in N \times N\). Then

[JEE Main 2024, 1 Feb (Shift 2)]

a

\(\text{ Only }{R}_{2}\text{ is an equivalence relation }\)

b

\({R}_{1}\text{ and }{R}_{2}\text{ both are equivalence relations }\)

c

\(\text{ Only }{R}_{1}\text{ is an equivalence relation }\)

d

\(\text{ Neither }{R}_{1}\text{ nor }{R}_{2}\text{ is an equivalence relation }\)

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