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Recent questions tagged kennethrosen
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Kenneth Rosen Edition 7th Exercise 2.3 Question 22 (Page No. 153)
Determine whether each of these functions is a bijection from$R$ to $R.$ $f(x) = 3x+4$ $f(x) = 3x^2+7$ $f(x) = (x+1)/(x+2)$ $f(x) = x^5+1$
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Apr 9
in
Set Theory & Algebra
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Pooja Khatri
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2
Kenneth Rosen Edition 7th Exercise 2.3 Question 21 (Page No. 153)
Give an explicit formula for a function from the set of integers to the set of positive integers that is onetoone, but not onto. onto, but not onetoone. onetoone and onto. neither onetoone nor onto.
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Apr 9
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Set Theory & Algebra
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Pooja Khatri
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3
Kenneth Rosen Edition 7th Exercise 2.3 Question 20 (Page No. 153)
Give an example of a function from $N$ to $N$ that is onetoone but not onto. onto but not onetoone. both onto and onetoone (but different from the identity function). neither onetoone nor onto.
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Apr 9
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Set Theory & Algebra
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Pooja Khatri
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4
Kenneth Rosen Edition 7th Exercise 2.3 Question 17 (Page No. 153)
Consider these functions from the set of teachers in a school. Under what conditions is the function onetoone if it assigns to a teacher his or her office. assigned bus to chaperone in a group of buses taking students on a field trip. salary. social security number
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Apr 9
in
Set Theory & Algebra
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Pooja Khatri
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10.8k
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5
Kenneth Rosen Edition 7th Exercise 2.3 Question 16 (Page No. 153)
Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function onetoone if it assigns to a student his or her mobile phone number. student identification number. final grade in the class. home town.
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Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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11
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6
Kenneth Rosen Edition 7th Exercise 2.3 Question 15 (Page No. 153)
Determine whether the function $f: Z \times Z \rightarrow Z$ is onto if $f(m,n) = m+n$ $f(m,n) = m^2+n^2.$ $f(m,n) = m.$ $f(m,n) = n.$ $f(m,n) = mn.$
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Set Theory & Algebra
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7
Kenneth Rosen Edition 7th Exercise 2.3 Question 14 (Page No. 153)
Determine whether $f: Z \times Z \rightarrow Z$ is onto if $f(m,n) = 2mn.$ $f(m,n) = m^2n^2.$ $f(m,n) = m+n+1.$ $f(m,n) = mn.$ $f(m,n) = m^24.$
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Apr 9
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Set Theory & Algebra
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Pooja Khatri
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3
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8
Kenneth Rosen Edition 7th Exercise 2.3 Question 11 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is onto? $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$
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Apr 9
in
Mathematical Logic
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Pooja Khatri
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23
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9
Kenneth Rosen Edition 7th Exercise 2.3 Question 13 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is onto?? $f(n) = n1$ $f(n) =n^2+1$ $f(n)= n^3$ $f(n) =\left \lceil n/2 \right \rceil$
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Apr 9
in
Set Theory & Algebra
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Pooja Khatri
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10.8k
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5
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10
Kenneth Rosen Edition 7th Exercise 2.3 Question 12 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is onetoone. $f(n) = n1$ $f(n) =n^2+1$ $f(n)= n^3$ $f(n) =\left \lceil n/2 \right \rceil$
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Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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6
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11
Kenneth Rosen Edition 7th Exercise 2.3 Question 10 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is onetoone. $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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5
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12
Kenneth Rosen Edition 7th Exercise 2.3 Question 9 (Page No. 153)
Find the values. $\left \lceil 3/4 \right \rceil$ $\left \lfloor 7/8 \right \rfloor$ $\left \lceil 3/4 \right \rceil$ $\left \lfloor 7/8 \right \rfloor$ $\left \lceil 3 \right \rceil$ ... $\left \lfloor 1/2.\left \lfloor 5/2 \right \rfloor \right \rfloor$
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Apr 9
in
Set Theory & Algebra
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Pooja Khatri
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4
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13
Kenneth Rosen Edition 7th Exercise 2.3 Question 8 (Page No. 153)
Find the values. $\left \lfloor1.1 \right \rfloor$ $\left \lceil 1.1 \right \rceil$ $\left \lfloor 0.1 \right \rfloor$ $\left \lceil 0.1 \right \rceil$ $\left \lceil 2.99 \right \rceil$ ... $\left \lceil \left \lfloor 1/2 \right \rfloor + \left \lceil 1/2 \right \rceil + 1/2 \right \rceil$
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Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
points)

6
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14
Kenneth Rosen Edition 7th Exercise 2.3 Question 1 (Page No. 153)
Find the domain and range of these functions. the function that assigns to each pair of positive integers the maximum of these two integers the function that assigns to each positive integer the number of the digits ... of the first $1$ in the string and that assigns the value 0 to a bit string consisting of all 0s
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Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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5
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15
Kenneth Rosen Edition 7th Exercise 2.3 Question 6 (Page No. 152)
Find the domain and range of these functions. the function that assigns to each pair of positive integers the first integer of the pair the function that assigns to each positive integer its largest decimal digit the function ... root of the integer the function that assigns to a bit string the longest string of ones in the string
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Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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8
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16
Kenneth Rosen Edition 7th Exercise 2.3 Question 5 (Page No. 152)
Find the domain and range of these functions. Note that in each case, to find the domain, determine the set of elements assigned values by the function. the function that assigns to each bit string the number of ... of 8 bits) the function that assigns to each positive integer the largest perfect square not exceeding this integer
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Apr 9
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Set Theory & Algebra
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Pooja Khatri
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17
Kenneth Rosen Edition 7th Exercise 2.3 Question 4 (Page No. 152)
Find the domain and range of these functions. Note that in each case, to find the domain, determine the set of elements assigned values by the function. the function that assigns to each nonnegative integer its last digit the ... of one bits in the string the function that assigns to a bit string the number of bits in the string
asked
Apr 9
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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5
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18
Kenneth Rosen Edition 7th Exercise 2.3 Question 3 (Page No. 152)
Determine whether $f$ is a function from the set of all bit strings to the set of integers if $f(S)$is the position of a $0$ bit in $S$. $f(S)$is the number of $1$ bits in $S$. $f(S)$is the smallest integer $i$ such that the $i$ th bit of $S$ is $1$ and $f(S)=0$ when $S$ is the empty string, the string with no bits.
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19
Kenneth Rosen Edition 7th Exercise 2.3 Question 2 (Page No. 152)
Determine whether $f$ is a function from $Z$ to $R$ if $f(n) = +n.$ $f(n) = \sqrt{n^2+1}.$ $f(n) = 1/(n^24).$
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20
Kenneth Rosen Edition 7th Exercise 2.3 Question 1 (Page No. 152)
Why is $f$ not a function from $R$ to $R$ if $f(x) =1 /x?$ $f(x) = \sqrt{x} ?$ $f(x) =± \sqrt{(x^2+1)}? $
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in
Set Theory & Algebra
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21
Kenneth Rosen Edition 7th Exercise 2.2 Question 37 (Page No. 137)
Show that if $A$ is a subset of a universal set $U$, then $A \oplus A = \phi.$ $A \oplus \phi = A.$ $A \oplus U = \sim A.$ $A \oplus \sim A= U.$
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Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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(
10.8k
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42
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kennethrosen
discretemathematics
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+2
votes
1
answer
22
Kenneth Rosen Edition 7th Exercise 2.2 Question 36 (Page No. 137)
Show that $A \oplus B = (AB) \cup (BA).$
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Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
points)

11
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23
Kenneth Rosen Edition 7th Exercise 2.2 Question 35 (Page No. 137)
Show that $A\oplus B = (A \cup B) – (A \cap B).$
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Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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9
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24
Kenneth Rosen Edition 7th Exercise 2.2 Question 32 (Page No. 137)
Find the symmetric difference of $\left \{ 1,3,5 \right \}$ and $\left \{ 1,2,3 \right \}.$
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Apr 6
in
Set Theory & Algebra
by
Pooja Khatri
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10.8k
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18
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25
Kenneth Rosen Edition 7th Exercise 2.2 Question 31 (Page No. 137)
Let $A$ and $B$ be sbusets of a universal set $U$. Show that $A \subseteq B$ if and only if $ \sim B \subseteq \sim A.$
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26
Kenneth Rosen Edition 7th Exercise 2.2 Question 30 (Page No. 137)
Can you conclude that $A = B$ if $A,B,$ and $C$ are sets such that $A \cup C = B \cup C?$ $A \cap C = B \cap C?$ $A \cup C = B\cup C$ and $A \cap C = B \cap C?$
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10.8k
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8
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27
Kenneth Rosen Edition 7th Exercise 2.2 Question 29 (Page No. 136)
What can you say about the sets $A$ and $B$ if we know that $A \cup B = A?$ $A \cap B = A?$ $A B = A?$ $A \cap B =B \cap A?$ $A –B = BA?$
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Set Theory & Algebra
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Pooja Khatri
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10.8k
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28
Kenneth Rosen Edition 7th Exercise 2.2 Question 28 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,C,$ and $D.$ $(A \cap B) \cup (C \cap D)$ $ \sim A \cup \sim B \cup \sim C \cup \sim D$ $A (B \cap C \cap D)$
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29
Kenneth Rosen Edition 7th Exercise 2.2 Question 27 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,$ and $C$. $A \cap (BC)$ $(A \cap B) \cup (A \cap C)$ $(A \cap \sim B) \cup (A \cap \sim C)$
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in
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10.8k
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11
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30
Kenneth Rosen Edition 7th Exercise 2.2 Question 26 (Page No. 136)
Draw the Venn diagrams for each of these combination sof the sets $A,B,$ and $C$. $A \cap (B \cup C)$ $\sim A \cap \sim B \cap \sim C$ $(AB) \cup (AC) \cup (BC)$
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in
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10.8k
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5
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