Which of the following relations in R is an equivalence relatilon? Options: A . &nbsp x R 1 y ⇔ | x | = | y | B . &nbsp x R 2 y ⇔ x ≥ y C . &nbsp x R 3 y ⇔ x y D . &nbsp x R 4 y ⇔ x < y

Which of the following relations in R is an equivalence relatilon?

Question -

Which of the following relations in R is an equivalence relatilon?

Options:

A .

x R_{1} y \Leftrightarrow | x | = | y |

B .

x R_{2} y \Leftrightarrow x \geq y

C .

x R_{3} y \Leftrightarrow \frac{x}{y}

D .

x R_{4} y \Leftrightarrow x < y

Answer: Option A
:
A
It is simple to check that only,

R_{1}

is an equivalence relation.

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