Consider the endorelation isPrereqFor, dened on the set of UMW courses. We say x

Question

Consider the endorelation isPrereqFor, dened on the set of UMW courses. We say x isPrereqFor y if passing course x is required before you are allowed to take course y. Otherwise, we say x isPrereqFor y. For example, ARTH 114 isPrereqFor CLAS 305, and CPSC 110 isPrereqFor CPSC 405 (since you can’t take 405 without 305, and you can’t take 305 without 220, and you can’t take 220 without 110), but CPSC 305 isPrereqFor CPSC 240 and MUTH 471 isPrereqFor MUTH 471. Is isPrereqFor a partial order? Explain why or why not. (Note: for maximum credit, give a good and complete answer.)

Explanation / Answer

For understand isPrereqFor a partial order need to create table

can’t take 405 without 305,

can’t take 305 without 220,

can’t take 220 without 110,

Since ARTH 114 is a direct isPrereqFor CLAS 305, so ARTH 114 come before CLAS 305.Also, CLAS 305 is a direct isPrereqFor CPSC 240, so in fact, ARTH 114 and CLAS 305 both come before taking CPSC 240.

So it has a basic property known as transitivity if any x is a direct PrereqFor of y, and y is a direct direct PrereqFor of subject z, then x is also an direct PrereqFor of z.

Here    ARTH 114 -------------> CLAS 305

         CLAS 305 ---------------> CPSC 240

so      ARTH 114 --------------> CPSC 240

Another property of the relation is that if a ------>b, then it is not the case that b --------> a. This property is called asymmetry

Here   ARTH 114 -------------> CLAS 305

         CLAS 305 ---------------> CPSC 240

So we can say Is isPrereqFor a partial order

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