210test2key

210test2key - i Also —-fa c[2 points Question 4b If a and...

This preview shows pages 1–6. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
[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 '
[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,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
[2 points] Question 4a. Suppose a \ and c | —. Prove that c b and a ' a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 > ar^ reldhvely pr\*ie. , <A-fa Sff*& intyefs "X Note. 2 . J I ^- /.' " / ^ t^ §> "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? "r 4-W xiumW '-2.- s )-S =3 No. No. Tlie-Wie+ (A^<S Ihl . <^J ^ ^^ M wifc\$^" € _ A = UN)...
View Full Document

{[ snackBarMessage ]}

Page1 / 6

210test2key - i Also —-fa c[2 points Question 4b If a and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online