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15) Determine whether each of the following is a bijection from R to R
18) Is 321 congruent to 469 mod 7?
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SHOW WORK 15) Determine whether each of the following is a bijection from R to R...
5. Determine whether each of these functions is a bijection from R to R. (a) /()=2x-10 (b)/(a) - 4 +4 (c)/(w) - (x + 1)/(x+2) (d)/(a) 7+1
2. Determine whether the given sets are countable or uncountable. Justify each answer with a bijection (or table like we did with Q+) or using results from class/textbook. (a) {0, 1, 2} * N (b) A = {(x, y) : x2 + y2 = 1} (c) {0, 1} R Che set of all 2-element subsets of N (e) Real numbers with decimal representations consists of all 1s. (f) The set of all functions from {0,1} to N
3. Determine algebraically whether each of the following functions is one-to-one. Show your work! (a) f(x) = 4x2 4x (b) g(x) 3x + 2 2x – 1
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1. (15) Characterize the following relations in terms of whether they are reflexive, irreflexive, symmetric, anti- symmetric, transitive, complete, any sort of ordering relation, and/or an equivalence relation. a. R CRX R with R = {(x,y)|x<y>} b. RCRXR with R= {(x, y)|x3 = y3} C. RSRXR with R = {(x, y) x2 + y2}
Problem 8. Given each pair of sets, come up with a formula for a bijection between them You do not need to prove your function is a bijection. Your formula should not be complicated by any means 1. From (0, 1) to (211, 2019) 2. From [0, 1) to (0, 1] 3. From NU (o) to N. 4. From the set of even numbers to 2 5. From the set of odd numbers to Z. 6. r2'2 7. From R...
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3. Relations - No Proofs! Determine (no proof needed!) whether each of the following relations R, S, T on the set of real numbers is reflexive, symmetric, antisymmet- ric, and/or transitive. a) x Ry iff 3 - y is positive: reflexive: symmetric: anti-symmetric: transitive: b) xSy iff 2 = 2y: reflexive: symmetric anti-symmetric: transitive: c) Ty iff zy 30: reflexive: symmetric: anti-symmetric transitive:
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15. In the original Star Trek, characters were separated by their rank and station on the Enterprise via differently colored uniforms. We wish to determine whether a character dying on the show was independent of their uniform color. The data on the number of characters seen with each color of uniform, along with whether they died, are given below. Alive Dead Blue 1297 Gold 469 Red 215 24 (a) Which test is appropriate? Why? (b) Write...
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Use the following to answer questions 1-4 Determine whether the firm reports each of the following items as part of cash, cash equivalents, or neither in the balance sheet. Item Cash, Cash equivalent, or neither Inventory for sale to customers 2. Investment with a maturity of 80 days at purchase 3 Three month US Treasury Bill 4. Bank deposits Use the following to answer questions 5-8 Bank Reconciliation: Identify whether the item should be added or subtracted...
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7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2
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7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2