question one: defined the following relation on A={0,2,5,6} Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 and are reflexive, simply enter 1, 2 as the answer.1) Which relations are reflexive? 2) R0={(0,6),(6,6),(6,2),(0,0),(0,2),(2,2),(5,5)} 3) R1={(6,6),(2,2),(5,5),(0,0),(0,6)} 4) R2={(0,6),(6,6),(0,0),(5,6),(6,5),(5,0),(5,5),(2,2),(0,5) 5) R3={(5,5),(0,0),(6,6),(2,2) 6) R4={(5,5),(6,2),(6,6),(0,0),(6,5),(2,6),(2,2)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric? 4) Which relations are transitive? 5) Which relations are equivalence relations? 6) Which relations are partial orders? question two :defined the following relation on A={0,1,5,6} Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 and are reflexive, simply enter 1, 2 as the answer. R0={(5,5),(0,0),(6,6),(1,1)} R1={(5,6),(5,0),(5,1),(0,6),(5,5),(0,1)} R2={(0,6),(6,0),(1,1),(0,0),(5,5),(6,6)} R3={(1,6),(6,5),(5,5),(1,0),(0,0),(1,1)} R4={(5,6),(0,1),(5,5),(6,1),(1,6),(1,0),(6,5)} let A={78,90,100,120,133,141,146,153} and R be an equivalence relation defined on A where aRb if and only if a=b mod 5 1.Show the partition of A defined by the equivalence classes of R
question one: defined the following relation on A={0,2,5,6} Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 and are reflexive, simply enter 1, 2 as the answer.1) Which relations are reflexive? 2) R0={(0,6),(6,6),(6,2),(0,0),(0,2),(2,2),(5,5)} 3) R1={(6,6),(2,2),(5,5),(0,0),(0,6)} 4) R2={(0,6),(6,6),(0,0),(5,6),(6,5),(5,0),(5,5),(2,2),(0,5) 5) R3={(5,5),(0,0),(6,6),(2,2) 6) R4={(5,5),(6,2),(6,6),(0,0),(6,5),(2,6),(2,2)} 1) Which relations are reflexive? 2) Which relations are symmetric? 3) Which relations are anti-symmetric? 4) Which relations are transitive? 5) Which relations are equivalence relations? 6) Which relations are partial orders?
question two :defined the following relation on A={0,1,5,6} Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R1 and R2 and are reflexive, simply enter 1, 2 as the answer.
R0={(5,5),(0,0),(6,6),(1,1)}
R1={(5,6),(5,0),(5,1),(0,6),(5,5),(0,1)}
R2={(0,6),(6,0),(1,1),(0,0),(5,5),(6,6)}
R3={(1,6),(6,5),(5,5),(1,0),(0,0),(1,1)}
R4={(5,6),(0,1),(5,5),(6,1),(1,6),(1,0),(6,5)}
let A={78,90,100,120,133,141,146,153} and R be an equivalence relation defined on A where aRb if and only if a=b mod 5 1.Show the partition of A defined by the equivalence classes of R
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