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.
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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.
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.
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.
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.
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.
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 1 of 3 Module 4 Homework