Theorem 8.1.3. If R and S are functional relations, then so is Sa R. We again first try to use the backward-forward method. Our proof begins and ends as usual: Proof. Let R and S be functional relations. Then SoR is a functional relation. We can apply the definition of functional relations: Proof. Let Rand S be functional relations. So So R is a relation such that each element in Dom(Se R) has a unique So R-refative. Then So R is a functional relation by Definition 8.1.1. We have to show first that SoR is indeed a relation and then that each element in Dom(So R) has a unique So R-relative: Proof. Let R and S be functional relations. Then SeRis a relation.

Theorem 8.1.3. If R and S are functional relations, then so is Sa R. We again first try to use the backward-forward method. Our proof begins and ends as usual: Proof. Let R and S be functional relations. Then SoR is a functional relation. We can apply the definition of functional relations: Proof. Let Rand S be functional relations. So So R is a relation such that each element in Dom(Se R) has a unique So R-refative. Then So R is a functional relation by Definition 8.1.1. We have to show first that SoR is indeed a relation and then that each element in Dom(So R) has a unique So R-relative: Proof. Let R and S be functional relations. Then SeRis a relation.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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