Question

Let R and S be relations defined on the set of {2,4,9,8}. R={(4,8),(9,2),(4,4),(9,9)}. S={(8,8),(2,2),(4,9),(4,4)}.

Answer each of the following questions.
R∘S={ }
S∘S={ }

Answer 1

To find R∘S, we need to compose the relations R and S. R∘S={(4,2),(9,8)}. To find S∘S, we need to compose the relation S with itself. S∘S={(8,8),(2,2),(4,8),(4,4)}.

Step-by-step explanation:

In this problem, we are given two relations R and S defined on a set of {2,4,9,8}. R={(4,8),(9,2),(4,4),(9,9)} and S={(8,8),(2,2),(4,9),(4,4)}. We need to find R∘S and S∘S.

To find R∘S, we need to compose the relations R and S. The composition of two relations is obtained by taking the cartesian product of the second component of each ordered pair in R with the first component of each ordered pair in S, when the second component of R matches the first component of S.

R∘S={(4,2),(9,8)}

To find S∘S, we need to compose the relation S with itself. S∘S={(8,8),(2,2),(4,8),(4,4)}