Answer to Question #14786 in Abstract Algebra for Sujata Roy

Question

The binary relation S=empty set on set A={1,2.3} is
a) neither reflexive nor symmetric
b) symmetric and reflexive
c) transitive and reflexive
d) transitive and symmetric

Answer 1

d) transitive and symmetric

In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c.
A binary relation R over a set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a.