mat300q1ans

# mat300q1ans - MAT 300 Mathematical Structures ANSWERS Quiz...

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Unformatted text preview: MAT 300 , Mathematical Structures ANSWERS Quiz 1 February 18, 2010 1. (5 points) Short-answer questions. (a) Complete the following definition: For sets A and B , A is a subset of B if for every x ∈ A , x ∈ B . (b) Negate the following statement and express the result in a positive form: “There exists an integer s such that s is odd and s is divisible by 5.” Answer: For every integer s , s is not odd (will accept s is even ) or s is not divisible by 5 . (c) Let N = { , 1 , 2 , 3 , ···} be the natural numbers. Is the following statement true or false? Explain. ∃ x ∈ N ∀ y ∈ N ( x + y > 100). Answer: The statement is true. If we pick, for example, x = 101 , then every natural number y satisfies y ≥ , so x + y ≥ 101 > 100. Let the sets B i ⊆ N be defined so that B i = { i,i + 1 ,i + 2 ,i + 3 } . (d) 7 \ i =5 B i = { 7 , 8 } . (e) B 3 \ B 6 = { 3 , 4 , 5 } . 2. (6 points) Suppose A , B , and C are sets. If A \ C ⊆ B , prove that A \ B ⊆ C ....
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mat300q1ans - MAT 300 Mathematical Structures ANSWERS Quiz...

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