For the given relation R on a set S, determine which are equivalence relations: (a) (i) S is the set of all rational number a R b iff a= b (ii) S is the set of all real numbers iff: (I) |a| = |b| (II) a ge b (b) (i) S is the set of all traingles in a plane a R b iff a is congrunet to b. (ii) S is the set of all triangles in a place a R b iff a and b have equal perimeters. (iii) S is the set of all people in India today, a R b iff a and b have same mother-tongue. (iv) S is the of all people in the world today aRb iff a and b have same mother-tongue. (v) S is the set of all people in the world today a R b iff a lives within 75 kilometres of b.

For the given relation R on a set S, determine which are equivalence r

1.	For the given relation R on a set S, determine which are equivalence relations: (a) (i) S is the set of all rational number a R b iff a= b (ii) S is the set of all real numbers iff: (I) \|a\| = \|b\| (II) a ge b (b) (i) S is the set of all traingles in a plane a R b iff a is congrunet to b. (ii) S is the set of all triangles in a place a R b iff a and b have equal perimeters. (iii) S is the set of all people in India today, a R b iff a and b have same mother-tongue. (iv) S is the of all people in the world today aRb iff a and b have same mother-tongue. (v) S is the set of all people in the world today a R b iff a lives within 75 kilometres of b.
Answer» ANSWER :(a) (i), (II) (B) (ii)