(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive. (b) Decide whether each of the following relations is transitive. [No justification is required - just write "yes" or "no" for each case.] (i) The relation R on Z defined by aRb if a + b + 1. (ii) The relation R on Z defined by aRb if a² = b². (iii) The relation R on Zx Z defined by (a, b)R(c, d) if ad = bc. (c) Let z be the complex number 4-3i. Find the following. [You do not need to show your working, but doing so may help you to gain marks if you make arithmetic errors.] (iv) z². (v) A complex number w such that wz = z.
(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive. (b) Decide whether each of the following relations is transitive. [No justification is required - just write "yes" or "no" for each case.] (i) The relation R on Z defined by aRb if a + b + 1. (ii) The relation R on Z defined by aRb if a² = b². (iii) The relation R on Zx Z defined by (a, b)R(c, d) if ad = bc. (c) Let z be the complex number 4-3i. Find the following. [You do not need to show your working, but doing so may help you to gain marks if you make arithmetic errors.] (iv) z². (v) A complex number w such that wz = z.
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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![(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive.
(b) Decide whether each of the following relations is transitive. [No justification is required - just
write "yes" or "no" for each case.]
(i) The relation R on Z defined by aRb if a + b + 1.
(ii) The relation R on Z defined by aRb if a² = b².
(iii) The relation R on Zx Z defined by (a, b)R(c,d) if ad = bc.
(c) Let z be the complex number 4-3i. Find the following. [You do not need to show your
working, but doing so may help you to gain marks if you make arithmetic errors.]
(iv) z².
(v) A complex number w such that wz = ż.
(d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N
such that x" is a real number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ec59470-7284-445f-830c-21983d8e4927%2Fb4e3cd74-63db-4063-89de-3c25cb13ffb4%2Fgas94yn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Suppose R is a relation on a set X. Define what it means to say that R is transitive.
(b) Decide whether each of the following relations is transitive. [No justification is required - just
write "yes" or "no" for each case.]
(i) The relation R on Z defined by aRb if a + b + 1.
(ii) The relation R on Z defined by aRb if a² = b².
(iii) The relation R on Zx Z defined by (a, b)R(c,d) if ad = bc.
(c) Let z be the complex number 4-3i. Find the following. [You do not need to show your
working, but doing so may help you to gain marks if you make arithmetic errors.]
(iv) z².
(v) A complex number w such that wz = ż.
(d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N
such that x" is a real number.
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