210test2key - i Also -fa ** c , [2 points] Question 4b. If...

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Math 210 Section Oil: Test #2 NAME: !_ This test has 6 pages. The points per page are 4, 5, 5, 4, 5, 5. [2 points] Question la. Compute gcd(161,196). = L-ltl + 35 = 4-35 + 2i 35T = 1-21 * 2i - i'H ^ - 2-1 +o [2 points] Question Ib. Write gcd(161, 196) as an integer linear combination of 161 and 196. 7 = 2L ~ W -^35- -20 -2/-3Sf2 / '- 2- 161 -S- 35" -Ss
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[3 points] Question 2a. For each of the following relations, determine whether it's a function with domain {1,2,3,4}. (i) {(1,1), (2,1), (3,2), (4,2), (3,4)} Mo eytttiu \~s [2 points] Question 2b. Suppose >1 and B are nonempty sets. Can A x B ever be a function from A to 5? Explain. sef of rf/l A/of if B ;s <^ 6^ ' M '
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[5 points] Question 3. Let A = (0, 1, 2, 3, 4, 5, 6}. Define / : A -»• A as follows: I 3x if 0 < 3x < 7 3x-7 if 7 < 3x < 14 3x - 14 if 14 < 3x < 21 ~ Express the inverse of / as a set of ordered pairs. -f (o)= O -F(a ) - G - = o s f -F^S) r 19 -H = 1 f Or foo), (1, 5)^(2,3), (3,
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[2 points] Question 4a. Suppose a \ and c | —. Prove that c b and a ' a
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Unformatted text preview: i Also -fa ** c , [2 points] Question 4b. If a and b are relatively prime integers, prove that gcd(a + 6, a 6) = 1 or 2. 4 C a &gt; ar^ reldhvely pr\*ie. , &lt;A-fa Sff*&amp; intyefs &quot;X Note. 2 . J I ^- /.' &quot; / ^ t^ &gt; &quot;i j, jrj r~ I * [5 points] Question 5. Prove that if n is an odd integer, then n 2 1 must be divisible by 8. / proofs fife fvf Y. arab n s 7 ,-s / W -ftf-fS ^n.X S + V [5 points] Question 6. Consider the function / from N \} to N defined by f(n] = the largest prime divisor of n. (i) Find /(n) for each n = 2, 3,. . . , 10. (ii) What is the range of /? (iii) Is / one-to-one? (iv) Is / onto? (v) Why did we not express / as a function from N to N? &quot;r 4-W xiumW '-2.- s )-S =3 No. No. Tlie-Wie+ (A^&lt;S Ihl . &lt;^J ^ ^^ M wifc$^&quot; _ A = UN)...
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210test2key - i Also -fa ** c , [2 points] Question 4b. If...

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