3. A proper subset of a set S is a subset of S which is not equal to S itself. Some people write "A CB" to mean "A is a proper subset of B", but other people use this notation in the same way as "AB"; to be unambiguous, it is better to write "AB" to mean "A is a proper subset of B".
3. A proper subset of a set S is a subset of S which is not equal to S itself. Some people write "A CB" to mean "A is a proper subset of B", but other people use this notation in the same way as "AB"; to be unambiguous, it is better to write "AB" to mean "A is a proper subset of B".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Help with three
![(a) {1,3,5,7,9,11,1
,...}.
(b) {-36,-25,-16, -9,-4,-1}.
3. A proper subset of a set S is a subset of S which is not equal to S itself. Some people
write "A <B" to mean "A is a proper subset of B", but other people use this notation in
the same way as "A ≤B"; to be unambiguous, it is better to write "AB" to mean “A
is a proper subset of B".
Write down all true statements of the form
by Ø, Z, {0, 1), and [0, 1].
4. Find all subsets of S = {0, 1, {0, 1}} which are not also elements of S.
(Another way of writing this problem could be "List all the elements of P(S)-S".)
5. Using the sets A = {1,2,3}, B = {3,4,5}, and C = {2,4,6} and the operations U (union),
n (intersection) and - (set difference), write down an expression that gives the set
{2,3,4,5).
6. A subset of the number line is drawn below and continues by the same pattern indefi-
nitely to the right.
-3 -2 -1
+
0
1
|||
Đ
2
{
3
B
Write down an expression for this set in the form U
NEN
1
"where the blanks can be filled in
✪
4
5
O
A
6
7. Let A = [0,2), B = (1,3], and C = (2,00). In each region of a Venn diagram such as the one
drawn below, write down the set of all real numbers that belong in that region. (They
are all either intervals, sets with only one element, or the empty set.)
A
7
Đ
8
8. Let A = {1,2}. List the elements of A x P(A).
9. Let P denote the open sentence "x € A" and let denote the open sentence "x € B".
(a) Write "x € A -B" in terms of P and Q, using logical operations to connect them.
(b) Suppose that P⇒ is true for any x. What is the relationship between sets A
and B?
9
10. Write the sentences below either in the form "If P, then Q" without changing the mean-
ing.
(a) Only the good die young.
(b) You must be this tall in order to go on this ride.
(c) You can't make an omelet without breaking a few eggs.
#
Đ
10
S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F232028c3-8426-43ce-b04a-a507a5240356%2F93bc38d4-193c-40f5-a16b-cced549d234b%2Fboc2xyb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) {1,3,5,7,9,11,1
,...}.
(b) {-36,-25,-16, -9,-4,-1}.
3. A proper subset of a set S is a subset of S which is not equal to S itself. Some people
write "A <B" to mean "A is a proper subset of B", but other people use this notation in
the same way as "A ≤B"; to be unambiguous, it is better to write "AB" to mean “A
is a proper subset of B".
Write down all true statements of the form
by Ø, Z, {0, 1), and [0, 1].
4. Find all subsets of S = {0, 1, {0, 1}} which are not also elements of S.
(Another way of writing this problem could be "List all the elements of P(S)-S".)
5. Using the sets A = {1,2,3}, B = {3,4,5}, and C = {2,4,6} and the operations U (union),
n (intersection) and - (set difference), write down an expression that gives the set
{2,3,4,5).
6. A subset of the number line is drawn below and continues by the same pattern indefi-
nitely to the right.
-3 -2 -1
+
0
1
|||
Đ
2
{
3
B
Write down an expression for this set in the form U
NEN
1
"where the blanks can be filled in
✪
4
5
O
A
6
7. Let A = [0,2), B = (1,3], and C = (2,00). In each region of a Venn diagram such as the one
drawn below, write down the set of all real numbers that belong in that region. (They
are all either intervals, sets with only one element, or the empty set.)
A
7
Đ
8
8. Let A = {1,2}. List the elements of A x P(A).
9. Let P denote the open sentence "x € A" and let denote the open sentence "x € B".
(a) Write "x € A -B" in terms of P and Q, using logical operations to connect them.
(b) Suppose that P⇒ is true for any x. What is the relationship between sets A
and B?
9
10. Write the sentences below either in the form "If P, then Q" without changing the mean-
ing.
(a) Only the good die young.
(b) You must be this tall in order to go on this ride.
(c) You can't make an omelet without breaking a few eggs.
#
Đ
10
S
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