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Matrices, Sets and Relations

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Let:
D = days of the week {M, T, W, R, F},
E = {Brian (B), Jim (J), Karen (K)} be the employees of a tutoring center at a University U = {Courses the tutoring center needs tutors for}
= {Calculus I (I), Calculus II (II), Calculus III (III), Computers I (C1), Computers II (C2), Precalculus (P)}.

We define the relation R from D into E by d R e, if employee e is scheduled to work on day d. We also define S from E into U by e r u, if employee e is capable of tutoring students in course u. If: Please view the attachment for the rest of the question.

Questions:
(a) Interpret the above matrices with respect to the above relations.
(b) Compute M_SoR, and use this matrix to determine which courses will have tutors available on which days.
(c) Multiply the above matrices using regular arithmetic. Can you interpret this result?

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This solution is comprised of a step-wise response which investigates the concepts of matrices, sets and relations. This response is detailed and well presented in a Word document which is attached.

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