Answer to Question #172603 in Discrete Mathematics for Prisy

Question

Let R be the relation on the set A = {1,2,3,4,5,6,7} defined by the rule (a,b) equivalent to R, if the integer (a-b) is divisible by 4,

List the elements of R and its inverse

Answer 1

Solution:

We note:

1-5=-4, 5-1=4, 2-6=-4, 6-2=4, 3-7=-4, 7-3=4, 1-1=0, 2-2=0, 3-3=0, 4-4=0, 5-5=0, 6-6=0, 7-7=0. Their difference is divisible by 4.

Hence, R = {(1,5)(5,1),(2,6),(6,2),(3,7),(7,3),(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7)}

Let inverse of R be denoted by S.

Then, S = {(5,1),(1,5),(6,2),(2,6),(7,3),(3,7),(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7)} = R