Answer to Question #185747 in Discrete Mathematics for Freda

Question

Let R be the relation on the set A {1,2,3,4,5,6,7} defined by the rule (a,b) elements of R if the integer product of (a,b) is divisible by 4. List the elements of R and its inverse?

Answer 1

Let $R$ be the relation on the set $A= \{1,2,3,4,5,6,7\}$ defined by the rule $(a,b)\in R$ if the integer product $ab$ is divisible by 4.

Let us list the elements of $R:$

$R=\{(1,4),(4,1), (2,4),(4,2),(2,6),(6,2), (3,4), (4,3), (4,4),$

$(4,5),(5,4),(4,6),(6,4),(4,7),(7,4)\}$

Let us list the elements of $R^{-1}:$

$R^{-1}=\{(a,b):(b,a)\in R\}=\{(4,1),(1,4),(4,2),(2,4),(6,2),(2,6), (4,3),$

$(3,4), (4,4), (5,4),(4,5),(6,4),(4,6),(7,4),(4,7)\}=R.$