Given magnitudes w, x, y, z, Euclid defines w: x

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Answered: Given magnitudes w, x, y, z, Euclid…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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7. Let A and B be sets, and let f: A → B and g: B –→ A be functions. Suppose that: • go f(a) = a for every a E A; fo g(b) : = b for every b E B. Prove that f is bijective.
2. Given the function Fx) -4 3*+3-2 al Determine the mappina notation for this function
Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z × Y, (x, y) ER means that 2 is an integer x+y 1. State explicitly which ordered pairs in Z x Y is in R 2. Draw the arrow diagram of the relation. 3. Is the relation a function?
Define a relation R from R to R as follows: For all (x, y) ER×R, (x, y) E R if, and only if, x = y² + 1. Prove that (17, -4) ER %3D
X 10. Let R be the set of fractions i.e., R = {x,y € Z, y ± 0}. = Let ~ be defined by X р - ~ y is an equivalence relation. if and only if xq = yp. Show q
2. Let C = D = {-3, –2, –1, 1, 2, 3} and define a relation S from C to D as follows: For all (x, y) e C x D, 1 (x, y) E S means that 1 is an integer. y a. Is 2 S 2? Is –1S – 1? Is (2, 2) e S? Is (2, –-2) e S? b. Write S as a set of ordered pairs.
answer 2 and 3
11. Let C= {O, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, y) E AXB, %3D %3D y+2 (x, y) e R means that is an integer. a. Is 1 R 2? Is 2 R 8? Is (1, 8) e R? Is (2, 6) e R ? b. Write R as a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram for R.
a) Let A, B, U and V be any sets such that A CU and BC V. Is (A × B) C (U x V)? Justify your answer. b) Suppose f:R → Z where f(x) = [2x – 11. i. If A = {x |1 < x < 4}, find f (A). ii. If B = {3,4,5,6,7}, find f (B). iii. If C = {-9,-8}, find f¯1(C). c) Let f:R → R be defined by f (x) = 2x² + 2x – 12. Is fone-to-one? Justify - your answer.
6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A→ B as follows: For all (x, y) e A × B, (x, y) E R if and only if that x/y > 1. Find out following: R in the enumeration form а. b. Domain of R с. Co-domain of R

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