Question: Let set A = {1, 2, 3, 4} and B = {5, 6, 7, 8} whereby relation R 1 = {(a, b) | a =

Let set A = {1, 2, 3, 4} and B = {5, 6, 7, 8} whereby relation R1 = {(a, b) | a = b - 1 } and R2 = {(a, b) | a + b 3}. a is an element of set A and b is an element of set B.

 Write the relation for R1 and R2 where these represent the relation from set A to set B. (4)
Based on question in (i), solve R1 - R2 and R2 - R1. (4)
Evaluate R1 R2 and R2 R1. (4)
Suppose R3 is a relation on the same set A, write the relation R3 = {(a, b) | a mod b = 1 }. (2)
Determine whether the relation R3 is reflexive, symmetric, anti-symmetric and transitive. (8)
Determine whether the relation R3 is an equivalence relation or partial order. Give reason for your answer. (2)

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