List of top Mathematics Questions on Types of Relations

Let \( R \) be a relation on \( \{1,2,3\} \) defined by \[ R=\{(1,1),(2,2),(3,3),(1,2)\} \] Identify the properties satisfied by \(R\).

Let a relation \( R \) be defined on the set of all natural numbers \( \mathbb{N} \) by the rule: \( (a, b) \in R \) if and only if \( a + b \) is an even number. This relation \( R \) is classified as an:

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: