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6. For every relation R: A --→ B, we defined Rº : B --→ A to be the relation given by x Rºy if and only if y Rx. We called Rº the converse relation of R. Prove that, given two relations R: A --→ B and S: B --→ C, we have that (R; S)° = S° ; Rº.

6. For every relation R: A --→ B, we defined Rº : B --→ A to be the relation given by x Rºy if and only if y Rx. We called Rº the converse relation of R. Prove that, given two relations R: A --→ B and S: B --→ C, we have that (R; S)° = S° ; Rº.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. For every relation R: A -- --→ B, we defined Rº: B --> A to be the relation given by x Rºy if and only if y Rx. We called Rº the converse relation of R. Prove that, given two relations R: A --→ B and S: B --→ C, we have that (R; S)° = S° ; R°.
Transcribed Image Text:6. For every relation R: A -- --→ B, we defined Rº: B --> A to be the relation given by x Rºy if and only if y Rx. We called Rº the converse relation of R. Prove that, given two relations R: A --→ B and S: B --→ C, we have that (R; S)° = S° ; R°.
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