Let A be the set of all students in the EECS department at the University of Mic

Question

Let A be the set of all students in the EECS department at the University of Michigan, AnnArbor. Determine if each of the following relations on A are reexive, transitive, symmetric,or antisymmetric.
a) R1 = {(a, b)|a and b submitted the same code for project 4 in EECS 281}
b) R2 = {(a, b)|a has given advice to b on course selection for the fall}
[NOTE: For part a) you may assume that partner projects are not done in EECS 281and that no one has gone against the rules (there is no one who is in violation of theHonor Code)]

Explanation / Answer

a) R1 = {(a, b)|a and b submitted the same code for project 4 in EECS 281}

Obviously a submitted the same code as a. Therefore R1 is reflexive.

If a submitted the same code as b, then b submitted the same code as a. R2 is symmetric and not antisymmetric.

If a submitted the same code as b, b submitted the same code as c, then a submitted the same code as c. So R1 is transitive.

a) R2 = {(a, b)|a has given advice to b on course selection for the fall}

Obviously a has given advice to a. Therefore R2 is reflexive.

If a gave advice to b, then b may not have given advice to a. R2 is neither symmetric nor antisymmetric.

If a has given advice to b, b has given advice to c, then it need not be true that a has given advice to c. So R2 is not transitive.

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