# 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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