Exercise - 1.2

. Discuss the following relations for reflexivity, symmetricity and transitivity: (i) The relation R defined on the set of all positive integers by “ mRn if m divides n ”. (ii) Let P denote the set of all straight lines in a plane. The relation R defined by “ ℓRm if ℓ is perpendicular to m ”. (iii) Let A be the set consisting of all the members of a family. The relation R defined by “ aRb if a is not a sister of b ”. (iv) Let A be the set consisting of all the female members of a family. The relation R defined by “ aRb if a is not a sister of b ”. (v) On the set of natural numbers the relation R defined by “ xRy if x + y = ”. . Let X = { a, b, c, d } and R = { ( a, a ) , ( b, b ) , ( a, c ) } . Write down the minimum number of ordered pairs to be included to R to make it (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence . Let A = { a, b, c } and R = { ( a, a ) , ( b, b ) , ( a, c ) } . Write down the minimum number of ordered pairs to be included to R to make it (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence . Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b . Prove that R is an equivalence relation. . On the set of natural numbers let R be the relation defined by aRb if a + b = . Write down the relation by listing all the pairs. Check whether it is (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence . Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai. . On the set of natural numbers let R be the relation defined by aRb if a + b ≤ . Write down the relation by listing all the pairs. Check whether it is (i) reflexive (ii) symmetric (iii) transitive (iv) equivalence