Question

Let R₁ and R₂ be the relations on {1,2,3,4} given by

R₁ = {(1,1), (1,2), (3,4), (4,2)}

R₂ = {(1,1), (2,1), (3,1), (4,4), (2,2)}

           

List the elements of R_{1 °} R₂ and R_{2 °} R₁

Answer 1

R 1 ° R 2 = {(1,1),(1,2),(2,1),(2,2),(3,1),(3,2),(4,2)}

There are transitions

1-1-1

1-1-2

2-1-1

2-1-2

3-1-1

3-1-2

4-4-2

R 2 ° R 1 = {(1,1),(1,2),(3,4),(4,1)(4,2)}

There are transitions

1-1-1

1-2-2

3-4-4

4-2-1

4-2-2