midterm-sample2

midterm-sample2 - ‘No large birds live on honey.’...

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MACM 101 Midterm Test 2 Some Day, 2007 This is a sample! Last Name First Name and Initials Student No. NO AIDS allowed. Answer ALL questions on the test paper. Use backs of sheets for scratch work. Total Marks: 100 1. Give a de±nition of the codomain of a function. [10] 2. Give a de±nition of an onto function. [10] 3. Let P ( x ), Q ( x ), and R ( x ) denote the following open statements: [16] P ( x ) : x 2 - 8 x + 15 = 0 Q ( x ) : x is odd R ( x ) : x > 0. For the universe of all integers, determine the truth or falsity of the following statement. If the statement is false, give a counterexample. x (( P ( x ) Q ( x )) R ( x )) . 4. Given premises: [12] ‘All hummingbirds are richly colored.’
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Unformatted text preview: ‘No large birds live on honey.’ ‘Birds that do not live on honey are dull in color.’ infer the conclusion ‘Hummingbirds are small.’ 5. Give de±nition, what it means that a function f is in O ( g ). [10] 6. State the principle of strong induction. [16] 7. What is a permutation of size r ? How to ±nd the number of permutations of size r from a set with n elements? [10] 8. Let A , B , and C be sets. Show that [16] ( A-B )-C ⊆ A-C. Draw Venn diagrams for both expressions....
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