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Let A, B, and C be subsets of a universal set U. (a) Draw a Venn diagram with A G B and B ≤ C. Does it appear that ACC? (b) Prove the following proposition: If AB and BCC, then ACC. Note: This may seem like an obvious result. However, one of the reasons for this exercise is to provide practice at properly writing a proof that one set is a subset of another set. So we should start the proof by assuming that AB and BC. Then we should choose an arbitrary element of A.

Let A, B, and C be subsets of a universal set U. (a) Draw a Venn diagram with A G B and B ≤ C. Does it appear that ACC? (b) Prove the following proposition: If AB and BCC, then ACC. Note: This may seem like an obvious result. However, one of the reasons for this exercise is to provide practice at properly writing a proof that one set is a subset of another set. So we should start the proof by assuming that AB and BC. Then we should choose an arbitrary element of A.

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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**Let \( A, B, \) and \( C \) be subsets of a universal set \( U \).** (a) Draw a Venn diagram with \( A \subseteq B \) and \( B \subseteq C \). Does it appear that \( A \subseteq C \)? (b) Prove the following proposition: If \( A \subseteq B \) and \( B \subseteq C \), then \( A \subseteq C \). **Note:** This may seem like an obvious result. However, one of the reasons for this exercise is to provide practice at properly writing a proof that one set is a subset of another set. So we should start the proof by assuming that \( A \subseteq B \) and \( B \subseteq C \). Then we should choose an arbitrary element of \( A \).
Transcribed Image Text:**Let \( A, B, \) and \( C \) be subsets of a universal set \( U \).** (a) Draw a Venn diagram with \( A \subseteq B \) and \( B \subseteq C \). Does it appear that \( A \subseteq C \)? (b) Prove the following proposition: If \( A \subseteq B \) and \( B \subseteq C \), then \( A \subseteq C \). **Note:** This may seem like an obvious result. However, one of the reasons for this exercise is to provide practice at properly writing a proof that one set is a subset of another set. So we should start the proof by assuming that \( A \subseteq B \) and \( B \subseteq C \). Then we should choose an arbitrary element of \( A \).
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