Let L be the set of all lines in the XY plane and R be the relation on

1.	Let L be the set of all lines in the XY plane and R be the relation on L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.
Answer» Prove it is reflexive, prove it is symmetric, prove it is transitive. Because it is reflexive, symmetric and transitive, so it is an equivalence relation. Set of lines related to the line y = 2x + 4 is y = 2x + k where k is any real number.

Let L be the set of all lines in the XY plane and R be the relation on L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

Answer»

Prove it is reflexive, prove it is symmetric, prove it is transitive.

Because it is reflexive, symmetric and transitive, so it is an equivalence relation.

Set of lines related to the line y = 2x + 4 is y = 2x + k where k is any real number.

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Let L be the set of all lines in the XY plane and R be the relation on L defined as R = {(L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y = 2x + 4.

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