Answer to Question #145430 in Discrete Mathematics for yasser

Question

write the relation on {a,b,c,d} in ordered pairs.

Answer 1

Let $X=\{a,b,c,d\}.$ By defenition, a biniry relation $\rho$ on a set $X$ is a subset of a Cartesian square $X\times X.$ In our case,

$X\times X=\{(a,a),(a,b),(a,c),(a,d),(b,a),(b,b),(b,c),(b,d),(c,a),(c,b),(c,c)(c,d),$

$(d,a),(d,b),(d,c),(d,d)\}$.

For example, $\rho=\{(a,a),(a,c),(a,d),(b,b),(b,c),(c,a),(c,b),(c,d),(d,d)\}$ is a binary relation on the set $X.$