Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 14.3, Problem 2E
To determine
The potential outside sphere.
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7. Let X, A, and B be arbitrary sets such that ACX and BC X. Prove AUB CX.
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
Chapter 14 Solutions
Advanced Engineering Mathematics
Ch. 14.1 - Prob. 1ECh. 14.1 - Prob. 2ECh. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11E
Ch. 14.1 - Prob. 12ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 22ECh. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 18ECh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - Prob. 9ECh. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14 - Prob. 1CRCh. 14 - Prob. 2CRCh. 14 - Prob. 3CRCh. 14 - Prob. 4CRCh. 14 - Prob. 7CRCh. 14 - Prob. 10CRCh. 14 - Prob. 11CRCh. 14 - Prob. 12CRCh. 14 - Prob. 14CRCh. 14 - Prob. 15CRCh. 14 - Prob. 16CRCh. 14 - Prob. 17CRCh. 14 - Prob. 19CRCh. 14 - Prob. 22CRCh. 14 - Prob. 24CR
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- 10. 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_forward5. 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_forward
- 8. Give three statements that are logically equivalent to x ≥ 0⇒ (x² = 0V −x < 0). You may use any equivalences that you like.arrow_forward3. 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_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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