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Recent questions tagged kennethrosen
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Kenneth Rosen Edition 7th Exercise 2.1 Question 10 (Page No. 125)
Determine whether each of these statements is true or false. $\phi$ $ \epsilon$ {$\phi$} $\phi$ $\epsilon$ {$\phi,$ { $\phi$}} {$\phi$} $ \epsilon$ {$ \phi$} {$\phi$} $\epsilon $ {{$\phi$}} {$\phi$} $\subset$ {$0$} {$0$} $\subset$ {$\phi$ , { $\phi$ }} {$\phi$} $\subset$ {{$\phi$ }, { $\phi$}}
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

15
views
kennethrosen
discretemathematics
settheory&algebra
+2
votes
1
answer
2
Kenneth Rosen Edition 7th Exercise 2.1 Question 9 (Page No. 125)
Determine whether each of these statements is true or false. $0$ $ \epsilon$ $\phi$ $\phi$ $\epsilon$ {$0$} {$0$} $ \subset$ {$ \phi$} $\phi$ $\subset$ {$0$} {$0$} $\epsilon$ {$0$} {$0$} $\subset$ {$0$} {$\phi$} $\subseteq$ {$\phi$}
asked
Apr 5
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

46
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kennethrosen
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0
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0
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3
Kenneth Rosen Edition 7th Exercise 2.1 Question 7 (Page No. 125)
For each of the following sets, determine whether 2 is anelement of that set. { $x \epsilon R$  $x$ is an integer greater than $1$ } {$x \epsilon R$  $x$ is the square of an integer} { $2$ ,{ $2$ }} {{ $2$ },{{ $2$ }}} {{ $2$ },{ $2$ ,{ $2$ }}} {{{ $2$ }}}
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
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kennethrosen
discretemathematics
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0
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0
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4
Kenneth Rosen Edition 7th Exercise 2.1 Question 6 (Page No. 125)
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.
asked
Apr 5
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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5
Kenneth Rosen Edition 7th Exercise 2.1 Question 5 (Page No. 125)
Determine whether each of these pairs of sets are equal. { $1,3,3,3,5,5,5,5,5$ }, { $5,3,1$ } {{ $1$ }}, { $1$ , { $1$ }} $\phi$, { $\phi$ }
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

8
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kennethrosen
discretemathematics
settheory&algebra
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0
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6
Kenneth Rosen Edition 7th Exercise 2.1 Question 4 (Page No. 125)
For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first,or neither is a subset of the other. the set of people who speak English, the ... fruits, the set of citrus fruits the set of students studying discrete mathematics, the set of students studying data structures
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
points)

5
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
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7
Kenneth Rosen Edition 7th Exercise 2.1 Question 3 (Page No. 125)
For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other. the set of airline flights from New York to New Delhi ... English, the set of people who speak Chinese he set of flying squirrels, the set of living creatures that can fly.
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

6
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kennethrosen
discretemathematics
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0
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8
Kenneth Rosen Edition 7th Exercise 2.1 Question 2 (Page No. 125)
Use set builder notation to give a description of each of these sets. { $0,3,6,9,12$ } { $3,2,1,0,1,2,3$ } { $ m,n,o,p$ }
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

8
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
9
Kenneth Rosen Edition 7th Exercise 2.1 Question 1 (Page No. 125)
List the numbers of these sets. { $x$  $x$ is a real number such that $x^2 =1$ } { $x$  $x$ is a positive integer less than 12 } { $x$  $x$ is the square of an integer and $x<100$ } { $x$  $x$ is an integer such that $x^2 =2$ }
asked
Apr 5
in
Set Theory & Algebra
by
Pooja Khatri
Boss
(
10.8k
points)

8
views
kennethrosen
discretemathematics
settheory&algebra
0
votes
0
answers
10
Kenneth Rosen Edition 7th Exercise 1.7 Question 42 (Page No. 92)
Prove that these four statements about the integer $n$ are equivalent: $n^2$is odd, $1−n$ is even, $n^3$ is odd, $n^2+1$ is even.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

29
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
11
Kenneth Rosen Edition 7th Exercise 1.7 Question 41 (Page No. 92)
Prove that if $n$ is an integer, these four statements are equivalent: $n$ is even, $n+1$ is odd, $3n+1$isodd, $3n$ is even.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
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12
Kenneth Rosen Edition 7th Exercise 1.7 Question 39 (Page No. 92)
Prove that at least one of the real numbers $a_1,a_2,...,a_n$ is greater than or equal to the average of these numbers.What kind of proof did you use?
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

13
views
kennethrosen
discretemathematics
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0
votes
0
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13
Kenneth Rosen Edition 7th Exercise 1.7 Question 38 (Page No. 92)
Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

15
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
14
Kenneth Rosen Edition 7th Exercise 1.7 Question 37 (Page No. 91)
Show that the propositions $p1,p2,p3,p4,$ and $p5$ can be shown to be equivalent by proving that the conditional statements $p1 \rightarrow p4$ , $p3 \rightarrow p1$ ,$p4 \rightarrow p2$ ,$p2 \rightarrow p5$, and $p5 \rightarrow p3$ are true.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

25
views
kennethrosen
discretemathematics
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propositionallogic
0
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15
Kenneth Rosen Edition 7th Exercise 1.7 Question 36 (Page No. 91)
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

13
views
kennethrosen
discretemathematics
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0
votes
0
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16
Kenneth Rosen Edition 7th Exercise 1.7 Question 35 (Page No. 91)
Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct? $\sqrt{x+3=3−x}$ is given; $x+3=x2−6x+9$, obtained by squaring both sides of(1); $0=x2−7x+6$, obtained by subtracting $x+3$ from both sides of(2); $0=(x−1)(x−6)$, ... hand side of(3); $x=1$ or $x=6$,which follows from(4) because $ab=0$ implies that $a=0$ or $b=0$.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

24
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
17
Kenneth Rosen Edition 7th Exercise 1.7 Question 34 (Page No. 91)
Is this reasoning for finding the solutions of the equation $\sqrt{2x^2−1=x}$ correct? $\sqrt{2x^2−1=x}$ is given; $2x^2−1=x^2$, obtained by squaring both sides of (1); $x^2−1=0$, obtained by subtracting $x^2$from both sides of (2); ... lefthand side of$x^2−1$; $x=1$ or $x=−1$,which follows because $ab=0$ implies that $a=0$ or $b=0$
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

13
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
18
Kenneth Rosen Edition 7th Exercise 1.7 Question 33 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is irrational, $3x+2$ is irrational, $x/2$ is irrational.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

10
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kennethrosen
discretemathematics
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0
votes
0
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19
Kenneth Rosen Edition 7th Exercise 1.7 Question 32 (Page No. 91)
Show that these statements about the real number $x$ are equivalent: $x$ is rational, $x/2$ is rational, $3x−1$ is rational.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

10
views
kennethrosen
discretemathematics
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0
votes
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20
Kenneth Rosen Edition 7th Exercise 1.7 Question 31 (Page No. 91)
Show that these statements about the integer $x$ are equivalent: $3x+2$ is even, $x+5$ is odd, $x^2$ is even
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

11
views
kennethrosen
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21
Kenneth Rosen Edition 7th Exercise 1.7 Question 30 (Page No. 91)
Show that these three statements are equivalent, where $a$ and $b$ are real numbers: $a$ is less than $b$, the average of $a$ and $b$ is greater than $a$, and the average of $a$ and $b$ is less than $b$.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

9
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
22
Kenneth Rosen Edition 7th Exercise 1.7 Question 29 (Page No. 91)
Prove or disprove that if $m$ and $n$ are integers such that $mn=1$, then either $m=1$ and $n=1$, or else $m=−1$ and $n=−1$.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
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0
votes
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23
Kenneth Rosen Edition 7th Exercise 1.7 Question 28 (Page No. 91)
Prove that $m^2 = n^2$ if and only if $m=n$ or m = n.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
answers
24
Kenneth Rosen Edition 7th Exercise 1.7 Question 27 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is odd if and only if $5n+6$ is odd.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

5
views
kennethrosen
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25
Kenneth Rosen Edition 7th Exercise 1.7 Question 26 (Page No. 91)
Prove that if $n$ is a positive integer, then $n$ is even if and only if $7n+4$ is even.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
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(
10.8k
points)

8
views
kennethrosen
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26
Kenneth Rosen Edition 7th Exercise 1.7 Question 25 (Page No. 91)
Use a proof by contradiction to show that there is no rational number $r$ for which $r^3+r+1=0$. [Hint:Assume that $r=a/b$ is a root, where $a$ and $b$ are integers and $a/b$ is in lowest terms. Obtain an equation involving integer $s$ by multiplying by $b^3$. Then look at whether $a$ and $b$ are each odd or even.]
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

15
views
kennethrosen
discretemathematics
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propositionallogic
0
votes
0
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27
Kenneth Rosen Edition 7th Exercise 1.7 Question 24 (Page No. 91)
Show that at least three of any $25$ days chosen must fall in the same month of the year.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

9
views
kennethrosen
discretemathematics
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0
votes
0
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28
Kenneth Rosen Edition 7th Exercise 1.7 Question 23 (Page No. 91)
Show that at least ten of any $64$ days chosen must fall on the same day of the week.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

11
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
0
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29
Kenneth Rosen Edition 7th Exercise 1.7 Question 22 (Page No. 91)
Show that if you pick three socks from a drawer containing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks.
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

11
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
votes
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30
Kenneth Rosen Edition 7th Exercise 1.7 Question 21 (Page No. 91)
Let $P(n)$ be the proposition “If $a$ and $b$ are positive real numbers, then $(a+b)n≥a^n+b^n.$” Prove that $P(1)$ is true. What kind of proof did you use?
asked
Apr 4
in
Mathematical Logic
by
Pooja Khatri
Boss
(
10.8k
points)

10
views
kennethrosen
discretemathematics
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