Let R₁ and R₂ be two relations defined on R by

a R₁ b Û ab $\ge 0$  and a R₂ b $\iff a\ge b$  

Then,

<p>For R₁, take a = 1, b = 0, c = -1</p><p><span contenteditable="false"> <math> <mrow> <mi>a</mi> <mi>b</mi> <mo>≥</mo> <mn>0</mn> <mo>, </mo> <mi>b</mi> <mi>c</mi> <mo>≥</mo> <mn>0</mn> </mrow> </math> </span>but AC &lt; 0</p><p>So R₁ is not an equivalence relation.</p><p>For R₂, it will not be symmetric.</p><p>So R₂ is also not an equivalence relation.</p><p>&nbsp;</p>

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