Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1 is parallel to I2}. What is the type of given relation?(a) Reflexive relation(b) Transitive relation(c) Symmetric relation(d) Equivalence relationI got this question in an internship interview.My question comes from Types of Relations in chapter Relations and Functions of Mathematics – Class 12

Let I be a set of all lines in a XY plane and R be a relation in I def

1.	Let I be a set of all lines in a XY plane and R be a relation in I defined as R = {(I1, I2):I1 is parallel to I2}. What is the type of given relation?(a) Reflexive relation(b) Transitive relation(c) Symmetric relation(d) Equivalence relationI got this question in an internship interview.My question comes from Types of Relations in chapter Relations and Functions of Mathematics – Class 12
Answer» Right answer is (d) EQUIVALENCE relation For explanation: This is an equivalence relation. A relation R is said to be an equivalence relation when it is REFLEXIVE, TRANSITIVE and symmetric. Reflexive: We KNOW that a line is always parallel to itself. This implies that I1 is parallel to I1 i.e. (I1, I2)∈R. Hence, it is a reflexive relation. Symmetric: Now if a line I1 \|\| I2 then the line I2 \|\| I1. Therefore, (I1, I2)∈R implies that (I2, I1)∈R. Hence, it is a symmetric relation. Transitive: If two lines (I1, I3) are parallel to a third line (I2) then they will be parallel to each other i.e. if (I1, I2) ∈R and (I2, I3) ∈R implies that (I1, I3) ∈R.

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