Basic College Mathematics With Early Integers (4th Edition)
4th Edition
ISBN: 9780135176931
Author: Elayn Martin-Gay
Publisher: PEARSON
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Chapter C, Problem 41E
To determine
To sketch: The Venn diagram representing the statement “Some roosters crow”.
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1. Write out the following sets as a list of elements. If necessary you may use ... in
your description.
{x EZ: |x|< 10 A x < 0}
{x ЄN: x ≤ 20 A x = 2y for some y = N}
{n EN: 3 | n^ 1 < n < 20}
{y Є Z: y² <0}
3. For each statement below, write an equivalent statement using the justification
given.
= y Є A or yЄ B by the definition of union
= y Є A or y Є B by the definition of set complement
= x = C and x & D by DeMorgan's Law
=Vx (x EnFxЄEUF) by definition of subset.
= (X CYUZ)A (YUZ CX) by definition of set equality
6. Let A, B, and C be arbitrary sets. Prove that A - (BNC) = (A - B) U (A – C)
Chapter C Solutions
Basic College Mathematics With Early Integers (4th Edition)
Ch. C - Prob. 1PCh. C - Prob. 2PCh. C - Prob. 3PCh. C - Prob. 4PCh. C - Prob. 5PCh. C - Prob. 6PCh. C - Prob. 1ECh. C - Prob. 2ECh. C - Prob. 3ECh. C - Prob. 4E
Ch. C - Prob. 5ECh. C - Prob. 6ECh. C - Prob. 7ECh. C - Prob. 8ECh. C - Prob. 9ECh. C - Prob. 10ECh. C - Prob. 11ECh. C - Prob. 12ECh. C - Prob. 13ECh. C - Prob. 14ECh. C - Prob. 15ECh. C - Prob. 16ECh. C - Prob. 17ECh. C - Prob. 18ECh. C - Prob. 19ECh. C - Prob. 20ECh. C - Prob. 21ECh. C - Prob. 22ECh. C - Prob. 23ECh. C - Prob. 24ECh. C - Prob. 25ECh. C - Prob. 26ECh. C - Prob. 27ECh. C - Prob. 28ECh. C - Prob. 29ECh. C - Prob. 30ECh. C - Prob. 31ECh. C - Prob. 32ECh. C - Prob. 33ECh. C - Prob. 34ECh. C - Prob. 35ECh. C - Prob. 36ECh. C - Prob. 37ECh. C - Prob. 38ECh. C - Prob. 39ECh. C - Prob. 40ECh. C - Prob. 41ECh. C - Prob. 42ECh. C - Prob. 43ECh. C - Prob. 44ECh. C - Use diagrams and deductive reasoning to solve each...Ch. C - Prob. 46ECh. C - Prob. 47ECh. C - Prob. 48ECh. C - Prob. 49ECh. C - Prob. 50ECh. C - Prob. 51ECh. C - Prob. 52ECh. C - Prob. 53ECh. C - Prob. 54ECh. C - Prob. 1PFECh. C - Prob. 2PFECh. C - Prob. 3PFECh. C - Prob. 4PFECh. C - Prob. 5PFECh. C - Simplify by performing the indicated...Ch. C - Prob. 7PFECh. C - Prob. 8PFECh. C - Prob. 9PFECh. C - Prob. 10PFECh. C - Prob. 11PFECh. C - Prob. 12PFECh. C - Prob. 13PFECh. C - Prob. 14PFECh. C - Prob. 15PFECh. C - Note: Exercises 1–41 review operations with...Ch. C - Note: Exercises 1–41 review operations with...Ch. C - Prob. 18PFECh. C - Prob. 19PFECh. C - Prob. 20PFECh. C - Prob. 21PFECh. C - Prob. 22PFECh. C - Prob. 23PFECh. C - Prob. 24PFECh. C - Prob. 25PFECh. C - Prob. 26PFECh. C - Prob. 27PFECh. C - Prob. 28PFECh. C - Prob. 29PFECh. C - Prob. 30PFECh. C - Prob. 31PFECh. C - Prob. 32PFECh. C - Prob. 33PFECh. C - Prob. 34PFECh. C - Prob. 35PFECh. C - Prob. 36PFECh. C - Prob. 37PFECh. C - Prob. 38PFECh. C - Prob. 39PFECh. C - Prob. 40PFECh. C - Prob. 41PFECh. C - Prob. 42PFECh. C - Prob. 43PFECh. C - Prob. 44PFECh. C - Prob. 45PFECh. C - Prob. 46PFECh. C - Prob. 47PFECh. C - Prob. 48PFECh. C - Prob. 49PFECh. C - Prob. 50PFECh. C - Prob. 51PFE
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- 2. Find the cardinality of each set. {x = Z: |x| ≤ 5} {-2, 1, 4, 7, 10,..., 52} {{7,9}, 2, {1, 2, 3, 4, 7}, {9}, {0}}arrow_forwardA system of inequalities is shown. y 5 3 2 1 X -5 -4 -3 -2 -1 0 1 2 3 4 5 -1- Which system is represented in the graph? Oy>-x²-x+1 y 2x²+3 -2 -3 тarrow_forwardWhich set of systems of equations represents the solution to the graph? -5 -4 -3 -2 Of(x) = x² + 2x + 1 g(x) = x²+1 f(x) = x²+2x+1 g(x) = x²-1 f(x) = −x² + 2x + 1 g(x) = x²+1 f(x) = x² + 2x + 1 g(x) = x²-1 -1 5 y 4 3 2 1 0 -1- -2 -3- -4. -5 1 2 3 4 5arrow_forward
- Which of the graphs below correctly solves for x in the equation -x² - 3x-1=-x-4? о 10 8 (0,2) -10 -8 -6 -2 2 4 6 8 10 (-4,-2) -2 + (0,2) (4,6) -10-8-6-4-2 -2 2 4 6 8 10 (-3, -1) -2 2 (1-5) -6 -8 -10 10 -10-8-6-4-2 2 6 8 10 (2,0)arrow_forwardUnit 1: Logic 1. Let P be the statement "x > 5” and let Q be the statement “y +3≤ x," and let R be the statement “y Є Z.” (a) Translate the following statements to English. (b) Negate the statements symbolically (c) Write the negated statements in English. The negations should not include any implications. • (QV¬R) AP • (P⇒¬Q) VR • (PVQ)¬R 2. Let R, S, and T be arbitrary statements. Write out truth tables for the following statements. Determine whether they are a tautology or a contradiction or neither, with justification. ⚫ (RAS) V (¬R ⇒ S) (R¬S) V (RAS) • (TA (SV¬R)) ^ [T⇒ (R^¬S)]arrow_forward10. Suppose the statement -R (SV-T) is false, and that S is true. What are the truth values of R and T? Justify your answer.arrow_forward
- 5. Rewrite the statements below as an implication (that is, in "if... then..." structure). n is an even integer, or n = 2k - 1 for some k Є Z. x²> 0 or x = 0. 6. Rewrite each statement below as a disjunction (an or statement). If I work in the summer, then I can take a vacation. • If x2 y.arrow_forward4. Negate the following sentences. Then (where appropriate) indicate whether the orig- inal statement is true, or the negation is true. ⚫ If I take linear algebra, then I will do my homework or go to class. • (x > 2 or x < −2) ⇒ |x| ≥ 2 • P⇒ (QVR) ⇒(¬PV QV R) Vn EN Em E Q (nm = 1) • Ex E N Vy & Z (x. y = 1)arrow_forward8. Give three statements that are logically equivalent to x ≥ 0⇒ (x² = 0V −x < 0). You may use any equivalences that you like.arrow_forward
- 3. Let P, Q, and R be arbitrary statements, and let x E R. Determine whether the statements below are equivalent using whatever method you like. • • -[-P → (QVR)] and ¬(¬P V Q) A¬R (PA¬Q) ⇒(¬PVS) and (SVP) VQ • x = 4 and √√√x=2 x = 4 and x2. = 16arrow_forward2. Claim events on a portfolio of insurance policies follow a Poisson process with parameter A. Individual claim amounts follow a distribution X with density: f(x)=0.0122re001, g>0. The insurance company calculates premiums using a premium loading of 45%. (a) Derive the moment generating function Mx(t).arrow_forward7. Write the inverse, converse, and contrapositive. Which are true? Which are false? If x is an even integer, then x² + 3x + 5 is an odd integer. If y 5n+1 for some natural number If a <0, then 2a < 0. n, then 5 y.arrow_forward
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