Let $ R $ be the relation over the set $ A $ of all straight lines in a plane such that $ l_1 \, R \, l_2 \iff l_1 $ is parallel to $ l_2 $. Then $ R $ is:

Question

cdquestions Admin · Accepted Answer

The relation R is defined as l 1 R l 2 &harr; l 1 is parallel to l 2 . To check if R is an equivalence relation, we need to verify the following properties: Reflexivity: A line is parallel to itself, so l 1 R l 1 holds for all l 1 , so the relation is reflexive. Symmetry: If l 1 is parallel to l 2 , then l 2 is parallel to l 1 , so the relation is symmetric. Transitivity: If l 1 is parallel to l 2 , and l 2 is parallel to l 3 , then l 1 is parallel to l 3 , so the relation is transitive. Since all three properties hold, the relation R is an equivalence relation.

Answer

<div>Symmetric</div>

Answer

An Equivalence relation

Answer

<div>Transitive</div>

Answer

<div>Reflexive</div>

Let \( R \) be the relation over the set \( A \) of all straight lines in a plane such that \( l_1 \, R \, l_2 \iff l_1 \) is parallel to \( l_2 \). Then \( R \) is:

The Correct Option is B

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