1) Assume R = {(0,3),(1,3),(1,1),(2,0),(1,0),(1,2)} on the set A =...

Question

# 1) Assume R = {(0,3),(1,3),(1,1),(2,0),(1,0),(1,2)} on the set A =...

1) Assume R = {(0,3),(1,3),(1,1),(2,0),(1,0),(1,2)} on the set A = {0,1,2,3}. Draw digraphs of R0, R1, R2, and R3.

2) For each of the following theorems, give an example of two sets R and S which satisfy the conditions. Then, prove or disprove the theorems. Note the bold and italics text.

a. If R and S are reflexive, then R ◦ S is reflexive.
b. If R and S are symmetric, then R ◦ S is reflexive. c. If R and S are transitive, then R ◦ S is transitive.

d. If R and S are not irreflexive, then R ◦ S is not reflexive.

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