# mathematical symbols

MAT 299 Module Four Homework General:  Before beginning this homework, be sure to read the textbook sections and the material in Module Four.  Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit.  You may copy and paste mathematical symbols from the statements of the questions into your solution. This document was created using the Arial Unicode font.  These problems are proprietary to SNHU COCE, and they may not be posted on any nonSNHU website.  The Institutional Release Statement in the course shell gives details about SNHU’s use of systems that compare student submissions to a database of online, SNHU, and other universities’ documents. SNHU MAT299 Page 1 of 3 Module 4 Homework 1. Suppose that a and b are real numbers. Prove that if 0 < 1/a < 1/b, then b < a. This problem is similar to examples and exercises in Section 3.1 of your SNHU MAT299 textbook. 2. Suppose that A ⊆ B and x ∈ A. Use the method of “proof by contrapositive” to show that if x ∉ B \ C, then x ∈ C. This problem is similar to examples and exercises in Section 3.1 of your SNHU MAT299 textbook. 3. Suppose that A \ B ⊆ C ∩ D and x ∈ A. Use the method of “proof by contradiction” to show that if x ∉ C, then x ∈ B. This problem is similar to examples and exercises in Section 3.2 of your SNHU MAT299 textbook. 4. Suppose that x is a negative real number and that x < 1/x. Prove that x < –1. This problem is similar to examples and exercises in Section 3.2 of your SNHU MAT299 textbook. 5. Suppose x is a real number. Prove that if x ≠ 2, then there is a real number y such that x = (2y + 1) / (y – 1). This problem is similar to examples and exercises in Section 3.3 of your SNHU MAT299 textbook. 6. Suppose that ℱ is a non-empty family of sets, B is a set, and ∀A ∈ ℱ (A ⊆ B). Is ∪ℱ ⊆ B? Either provide a proof to show that this is true or provide a counterexample to show that this is false. This problem is similar to examples and exercises in Section 3.3 of your SNHU MAT299 textbook. SNHU MAT299 Page 2 of 3 Module 4 Homework SNHU MAT299 Page 3 of 3 Module 4 Homework
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