Question

let a relation r be defined on the set of all real numbers by a r b <=> 1 + ab > 0 thus r is ?

Answer 1

Answer:

is reflexive because a*a for any real number except 0 will be positive hence >0, and if a=0 then a*a + 1 >0. b. if a*b + 1 > 0 then b*a + 1 will also be > 0, hence symmetric. Hence, the given relation is reflexive and symmetric but not transitive.