mt1-sol

# mt1-sol - Math 55-2 Midterm 1 Rob Bayer July 9 2009 You...

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Unformatted text preview: Math 55-2 Midterm 1 Rob Bayer July 9, 2009 You have until 3:30pm to complete this test. No calculators, books, notes, or consultation with other members of the class are permitted. Your exam should have 3 pages. Unsupported or improperly supported answers will receive no credit. Name: 1 10 2 15 3 15 4 15 5 15 6 15 7 15 Total 100 1 1. (10 pts) Short answer. You need not show any work for this section (a) Complete each of the following definitions. Note that there are many possible answers to some of these questions and any mathematically correct definition will receive full credit. i. A compound proposition is a tautology iff It is always True ii. f : A → B is injective (one-to-one) iff f ( x ) = f ( y ) ⇒ x = y iii. If A ⊆ dom ( f ), then f ( A ) = { y : ∃ x ∈ Af ( x ) = y } iv. f : A → B is surjective (onto) iff ∀ y ∃ xf ( x ) = y v. a | b (“a divides b”) iff ∃ k ∈ Z ( b = ak ) vi. a,b are relatively prime (coprime) iff gcd( a,b ) = 1 (b) Order the following in increasing order of size: R , N , Z , P , Q , R- N (here P is the set of all primes). Note that some sets may be the same size as others, and you should be sure to indicate that....
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## This note was uploaded on 08/31/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.

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mt1-sol - Math 55-2 Midterm 1 Rob Bayer July 9 2009 You...

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