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Recent questions tagged kennethrosen
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Kenneth Rosen Edition 7th Exercise 2.2 Question 25 (Page No. 136)
Let $A = \left \{ 0,2,4,6,8,10 \right \}, B=\left \{ 0,1,2,3,4,5,6 \right \},$ and $C =\left \{ 4,5,6,7,8,9,10 \right \}.$ Find $A \cap B \cap C.$ $A \cup B \cup C.$ $(A \cup B) \cap C.$ $(A \cap B) \cup C.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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8
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kennethrosen
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2
Kenneth Rosen Edition 7th Exercise 2.2 Question 24 (Page No. 136)
Let $A, B$ and $C$ be sets. Show that $(AB)C = (AC)(BC).$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
points)

15
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kennethrosen
discretemathematics
settheory&algebra
0
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0
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3
Kenneth Rosen Edition 7th Exercise 2.2 Question 23 (Page No. 136)
Prove the first distributive law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup(B \cap C) = (A \cup B) \cap (A \cup C).$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
0
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0
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4
Kenneth Rosen Edition 7th Exercise 2.2 Question 22 (Page No. 136)
Prove the second associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cap C) = (A \cap B) \cap C.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
5
Kenneth Rosen Edition 7th Exercise 2.2 Question 21 (Page No. 136)
Prove the first associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cup C)= (A \cup B) \cup C.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

56
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
6
Kenneth Rosen Edition 7th Exercise 2.2 Question 20 (Page No. 136)
Show that if $A$ and $B$ are sets with $A \subseteq B,$ then $A \cup B = B$ $A \cap B = A$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
0
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0
answers
7
Kenneth Rosen Edition 7th Exercise 2.2 Question 19 (Page No. 136)
Show that if $A$ and $B$ are sets, then $AB = A \cap \sim B.$ $(A \cap B) \cup (A \cap \sim B)= A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
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8
Kenneth Rosen Edition 7th Exercise 2.2 Question 18 (Page No. 136)
Let $A,B,$ and $C$ be sets, Show that $(A \cup B) \subseteq (A \cup B \cup C),$ $(A \cap B \cap C) \subseteq (A \cap B.)$ $(AB)C \subseteq AC.$ $(AC) \cap (CB) = \phi.$ $(BA) \cup (CA) = (B \cup C) A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
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0
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9
Kenneth Rosen Edition 7th Exercise 2.2 Question 17 (Page No. 136)
Show that if $A,B,$ and $C$ are sets, then $ \sim (A \cap B \cap C) = \sim A \cup \sim B \cup \sim C$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
10
Kenneth Rosen Edition 7th Exercise 2.2 Question 16 (Page No. 136)
Let $A$ and $B$ be sets. Show that $(A \cap B) \subseteq A.$ $A \subseteq (A \subseteq B.)$ $AB \subseteq A.$ $A \cap(BA) = \phi$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
11
Kenneth Rosen Edition 7th Exercise 2.2 Question 15 (Page No. 136)
rove the second De Morgan law in Table 1 by showing that if $A$ and $B$ are sets, then $\sim (A \cup B) = (\sim A \cap \sim B)$ by showing each side is a subset of the other side. using a membership table.
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
12
Kenneth Rosen Edition 7th Exercise 2.2 Question 14 (Page No. 136)
Find the sets $A$ and $B$ if $AB=\left \{ 1,5,7,8 \right \}, BA=\left \{ 2,10 \right \},$ and $A \cap B=\left \{ 3,6,9 \right \}.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
13
Kenneth Rosen Edition 7th Exercise 2.2 Question 13 (Page No. 136)
Prove the second absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cap (A \cup B) = A$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

4
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
14
Kenneth Rosen Edition 7th Exercise 2.2 Question 12 (Page No. 136)
Prove the first absorption law from Table 1 by showing that if $A$ and $B$ are sets, then $A \cup (A \cup B) = A$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
15
Kenneth Rosen Edition 7th Exercise 2.2 Question 11 (Page No. 136)
Let $A$ and $B$ be sets. Prove the commutative laws from Table 1 by showing that $A \cup B = B \cup A.$ $A \cap B = B \cap A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

4
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
16
Kenneth Rosen Edition 7th Exercise 2.2 Question 10 (Page No. 136)
Show that $A \phi = A.$ $\phiA=\phi$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
17
Kenneth Rosen Edition 7th Exercise 2.2 Question 9 (Page No. 136)
Prove the complement laws in Table 1 by showing that $A \cup \sim A = U.$ $A \cap \sim A=\phi.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

4
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
18
Kenneth Rosen Edition 7th Exercise 2.2 Question 8 (Page No. 136)
Prove the idempotent laws in Table 1 by showing that $A \cup A = A.$ $A \cap A=A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
19
Kenneth Rosen Edition 7th Exercise 2.2 Question 7 (Page No. 136)
Prove the domination laws in Table 1 by showing that $A \cup U = U.$ $A \cap \phi=\phi.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

3
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
20
Kenneth Rosen Edition 7th Exercise 2.2 Question 6 (Page No. 136)
Prove the identity laws in Table 1 by showing that $A \cup \phi = A.$ $A \cap U=A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
21
Kenneth Rosen Edition 7th Exercise 2.2 Question 5 (Page No. 136)
Prove the complement law in Table 1 by showing That $\sim \sim A = A.$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

11
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
1
answer
22
Kenneth Rosen Edition 7th Exercise 2.2 Question 4 (Page No. 136)
Let $A= \left \{ a,b,c,d,e \right \}$ and $B= \left \{ a,b,c,d,e,f,g,h \right \}$. Find $A \cup B$ $A \cap B$ $AB$ $BA$
asked
Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

19
views
kennethrosen
discretemathematics
settheory&algebra
easy
+1
vote
0
answers
23
Kenneth Rosen Edition 7th Exercise 2.2 Question 3 (Page No. 136)
Let $A = \left \{ 1,2,3,4,5 \right \}$ and $B= \left \{ 0,3,6 \right \}$ .Find $A \cup B$ $A \cap B$ $AB$ $BA$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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24
Kenneth Rosen Edition 7th Exercise 2.2 Question 2 (Page No. 136)
Suppose that $A$ is the set of sophomores at your school and $B$ is the set of students in discrete mathematics at your school. Express each of these sets in terms of $A$ and $B$ . the set of ... are taking discrete mathematics the set of students at your school who either are not sophomores or are not taking discrete mathematics
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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25
Kenneth Rosen Edition 7th Exercise 2.2 Question 1 (Page No. 136)
Let $A$ be the set of students who live within one mile of school and let $B$ be the set of students who walk to classes. Describe the students in each of these sets. $A \cap B$ $A \cup B$ $A B$ $BA$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

4
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
26
Kenneth Rosen Edition 7th Exercise 2.1 Question 45 (Page No. 126)
The defining property of an ordered pair is that two ordered pairs are equal if and only if their first elements are equal and their second elements are equal. Surprisingly, instead of taking the ordered pair as a primitive concept, we can construct ordered pairs ... $a = c$ and $b=d.$]
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
difficult
0
votes
0
answers
27
Kenneth Rosen Edition 7th Exercise 2.1 Question 44 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^3>=1$ $Q(x) : x^2=2$ $R(x) : x<x^2$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

10
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
28
Kenneth Rosen Edition 7th Exercise 2.1 Question 43 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^2<3$ $Q(x) : x^2 >x$ $R(x): 2x+1 = 0$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

8
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kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
29
Kenneth Rosen Edition 7th Exercise 2.1 Question 42 (Page No. 126)
Translate each of these quantifications into English and determine is truth value. $\exists x$ $\epsilon$ $R(x^3 = 1)$ $\exists x$ $\epsilon$ $Z (x+1>x)$ $\forall x$ $\epsilon$ $(x1)$ $\epsilon$ Z $\forall x$ $\epsilon$ $Z (x^2 $ $\epsilon$ $Z)$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

7
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
30
Kenneth Rosen Edition 7th Exercise 2.1 Question 41 (Page No. 126)
Translate each of these quantifications into English and determine is truth value. $\forall x$ $\epsilon$ $(x^2 \neq 1)$ $\exists x$ $\epsilon$ $Z(x^2 =2) $ $\forall x$ $\epsilon$ $(x^2>0)$ $\forall x$ $\epsilon$ $R(x^2=x)$
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

3
views
kennethrosen
discretemathematics
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