7 Let A the set of courses required for your degree Let the

7. Let A = the set of courses required for your degree. Let the relation R be defined on A by course x is related to course y if course x is a prerequisite of course y. Explain why this relation is a antisymmetric relation. Is this relation a transitive relation? Explain

Solution

A relation is an antisymmetric relation if xRy then yRx is not true.

So here if course x is a prerequisite of couse y then it is not a logical statement tht course y will also be a prerequisite of course y. For example if course humanity is prerequisite to course Psychology, then this is not the case that Psychology would also be a prerequisite to course humanity.

So R is antisymmetric.

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Again as course x is prerequisite for course y and course y is a prerequisite for course z, then surely x will also be a prerequisite for course z also.

Thus R is a transitive relation here because if xRy and yRz then xRz here.