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RELATIONS Let C = (0, 1, 2) and D= (2, 4, 6, 8) and define a relation R from A to B as follows: Fo all (x, y) = AX B. (x, y) E R means that y+2 X a. Is 1 R 2? Is 2 8? Is (1,8) € R? Is (2, 6) € R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. is an integer.

RELATIONS Let C = (0, 1, 2) and D= (2, 4, 6, 8) and define a relation R from A to B as follows: Fo all (x, y) = AX B. (x, y) E R means that y+2 X a. Is 1 R 2? Is 2 8? Is (1,8) € R? Is (2, 6) € R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. is an integer.

Advanced Engineering Mathematics
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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RELATIONS Let C = (0, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, у) € Ax В. (x, y) E Rmeans that у+2 is an integer. a. Is 1 R 2? Is 2 8? Is (1, 8) E R? Is (2, 6) E R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram of R. Define a relation A from Rto Ras follows: For all (x, y) ERXR, (x, y) E A means that x y a. Is 57 A 53? Is (-17) A (-14)? Is (14, 14) E A? Is (-35, 1) E A? b. Draw the graph of A in the Cartesian plane. ARROW DIAGRAM OF A RELATION Let C = (0, 1, 2} and D = {2, 4, 6, 8} and define a relation R from A to B as follows: For all (x, у) € Ax В. (x, V) E Rmeans that +2 is an integer. a Is 1 R 2? Is 2 8? Is (1, 8) E R? Is (2, 6) E R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram of R. FUNCTIONS a. Find all relations from {a, b, c} to (u, v). b. Find all functions from {a, b, c} to {u, v). c. What fraction of the relations from {a, b, c) to (u, v) are functions? Let X = {a, b, c} and Y = {1, 2, 3, 4). Define a function Ffrom X to Yby the arrow diagram below.
Transcribed Image Text:RELATIONS Let C = (0, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, у) € Ax В. (x, y) E Rmeans that у+2 is an integer. a. Is 1 R 2? Is 2 8? Is (1, 8) E R? Is (2, 6) E R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram of R. Define a relation A from Rto Ras follows: For all (x, y) ERXR, (x, y) E A means that x y a. Is 57 A 53? Is (-17) A (-14)? Is (14, 14) E A? Is (-35, 1) E A? b. Draw the graph of A in the Cartesian plane. ARROW DIAGRAM OF A RELATION Let C = (0, 1, 2} and D = {2, 4, 6, 8} and define a relation R from A to B as follows: For all (x, у) € Ax В. (x, V) E Rmeans that +2 is an integer. a Is 1 R 2? Is 2 8? Is (1, 8) E R? Is (2, 6) E R? b. Write Ras a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram of R. FUNCTIONS a. Find all relations from {a, b, c} to (u, v). b. Find all functions from {a, b, c} to {u, v). c. What fraction of the relations from {a, b, c) to (u, v) are functions? Let X = {a, b, c} and Y = {1, 2, 3, 4). Define a function Ffrom X to Yby the arrow diagram below.
Let X = {a, b, c} and Y= {1, 2, 3, 4). Define a function F from Xto Yby the arrow diagram below. %3D X f Y •1 b. 3 •4 a. Write the domain and co-domain of F. b. Find F(a), F(b), and F(c). c. Represent Fas a set of ordered pairs. EQUALITY OF FUNCTIONS Let A = {0, 1, 2, 3} and define functions Fand G from A to A by the following formulas: For all xE A, F(x) = (x + 4)² and G(x) = (x² + 3x + 1). Is F= G? Explain.
Transcribed Image Text:Let X = {a, b, c} and Y= {1, 2, 3, 4). Define a function F from Xto Yby the arrow diagram below. %3D X f Y •1 b. 3 •4 a. Write the domain and co-domain of F. b. Find F(a), F(b), and F(c). c. Represent Fas a set of ordered pairs. EQUALITY OF FUNCTIONS Let A = {0, 1, 2, 3} and define functions Fand G from A to A by the following formulas: For all xE A, F(x) = (x + 4)² and G(x) = (x² + 3x + 1). Is F= G? Explain.
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