 Hello and welcome to the session, let us understand the following question which says, let L be the set of all lines in x, y plane and R be the relation in L, defined as R is equal to L1 and L2 such that L1 is parallel to L2, show that R is an equivalent relation. Find the set of all lines related to the line y is equal to 2x plus 4. Now let's write the solution, let L be the set of all lines in x, y plane. Given to us R is equal to ordered pair of L1 and L2 such that L1 is parallel to L2. Let us check for reflexivity belongs to L because an L2 L2 by definition of R conductivity L2 L3 belongs to L2 L3. Now the second part of the question says,