1. List the elements of each of the following sets by using the roster method. (a) The set of all days in a week that begin with the letter T. (b) The set of all positive integers less than 12 and greater than or equal to 6. (c) The set of all positive integers greater than 12 or less than or equal to 6.
1. List the elements of each of the following sets by using the roster method. (a) The set of all days in a week that begin with the letter T. (b) The set of all positive integers less than 12 and greater than or equal to 6. (c) The set of all positive integers greater than 12 or less than or equal to 6.
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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![Homework Exercises
1. List the elements of each of the following sets by using the roster method.
(a) The set of all days in a week that begin with the letter T.
(b) The set of all positive integers less than 12 and greater than or equal to 6.
(c) The set of all positive integers greater than 12 or less than or equal to 6.
(d) The set of all positive integers greater than 12 and less than or equal to 6.
(e) {x|x € N, x is odd, and x < 15}
(f) {x|x € Z and 2x² + 5x − 3 = 0}
(g) {x|x € Q and 2x² + 5x − 3 = 0}
(h) {z z E C and zª = 1}
(i) {(x, y)] x ≤ Z, y € Z, and 0 < x < y < 4}
2. Use set-builder notation to give a description of each of the following sets. Use mathematical
symbols wherever possible.
(a) {1, 2, 3, 4, 5}
(b) {a, e, i, o, u}
(c) {0, 5, 10, ...}
(d) The half-open interval [-3, 5)
(e) {..., -2, -, 0, ñ, 2π, ... }
(†) {1,2,3,1,3}}
'2'3'4'5
3. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6} and D = {4, 6, 8}. Determine which of
these sets are subsets of which other of these sets. Write your answers using the notation for
subset.
4. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {2, 2, 6, 2, 6}, D = {8, 6, 4}, and E = {8}.
Determine which of these sets are proper subsets of which other of these sets. Write your
answers using the notation for proper subset.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa03548f-393b-48a8-9f38-d1b27e81efe3%2Feb710ee5-d3d6-4944-94da-0fe197c93db5%2Fd406mu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Homework Exercises
1. List the elements of each of the following sets by using the roster method.
(a) The set of all days in a week that begin with the letter T.
(b) The set of all positive integers less than 12 and greater than or equal to 6.
(c) The set of all positive integers greater than 12 or less than or equal to 6.
(d) The set of all positive integers greater than 12 and less than or equal to 6.
(e) {x|x € N, x is odd, and x < 15}
(f) {x|x € Z and 2x² + 5x − 3 = 0}
(g) {x|x € Q and 2x² + 5x − 3 = 0}
(h) {z z E C and zª = 1}
(i) {(x, y)] x ≤ Z, y € Z, and 0 < x < y < 4}
2. Use set-builder notation to give a description of each of the following sets. Use mathematical
symbols wherever possible.
(a) {1, 2, 3, 4, 5}
(b) {a, e, i, o, u}
(c) {0, 5, 10, ...}
(d) The half-open interval [-3, 5)
(e) {..., -2, -, 0, ñ, 2π, ... }
(†) {1,2,3,1,3}}
'2'3'4'5
3. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6} and D = {4, 6, 8}. Determine which of
these sets are subsets of which other of these sets. Write your answers using the notation for
subset.
4. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {2, 2, 6, 2, 6}, D = {8, 6, 4}, and E = {8}.
Determine which of these sets are proper subsets of which other of these sets. Write your
answers using the notation for proper subset.
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