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Disprove: For any relations R and S, ran(S o R) = ran(S). Prove or disprove: If R and S are equivalence relations on A, then So R is an equivalence relation on A. Justify your answer.

Disprove: For any relations R and S, ran(S o R) = ran(S). Prove or disprove: If R and S are equivalence relations on A, then So R is an equivalence relation on A. Justify your answer.

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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Write all answers clearly. Proofs should be CLEAR, COHERENT, COMPLETE, and CONCISE. Let A, B, and C be sets. 1. Prove: If AC B then AN CC BnC. 2. Disprove: If ANCC BNC, then A C B. 3. Disprove: For any relations R and S, ran(S o R) = ran(S). 4. Prove or disprove: If R and S are equivalence relations on A, then So R is an equivalence relation on A. Justify your answer.
Transcribed Image Text:Write all answers clearly. Proofs should be CLEAR, COHERENT, COMPLETE, and CONCISE. Let A, B, and C be sets. 1. Prove: If AC B then AN CC BnC. 2. Disprove: If ANCC BNC, then A C B. 3. Disprove: For any relations R and S, ran(S o R) = ran(S). 4. Prove or disprove: If R and S are equivalence relations on A, then So R is an equivalence relation on A. Justify your answer.
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