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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 $A \cup B$ $A \cap B$ $AB$ $BA$
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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 $A \cup B$ $A \cap B$ $AB$ $BA$
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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
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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. $A \cap B$ $A \cup B$ $A B$ $BA$
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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 $b=d.$]
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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. $P(x) : x^3>=1$ $Q(x) : x^2=2$ $R(x) : x<x^2$
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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. $P(x) : x^2<3$ $Q(x) : x^2 >x$ $R(x): 2x+1 = 0$
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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 $ $\epsilon$ $Z)$
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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) $ $\forall x$ $\epsilon$ $(x^2>0)$ $\forall x$ $\epsilon$ $R(x^2=x)$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 40 (Page No. 126)
Explain why $(A \times B) \times (C \times D)$ and $A \times (B \times C) \times D$ are not the same.
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Kenneth Rosen Edition 7th Exercise 2.1 Question 39 (Page No. 126)
Explain why $A \times B \times C$ and $(A \times B) \times C$ are not the same.
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Kenneth Rosen Edition 7th Exercise 2.1 Question 38 (Page No. 126)
Show that $A \times B \neq B \times A$, when $A$ and $B$ are nonempty. unless $A = B.$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 37 (Page No. 126)
How many different elements does $A^n$ have when $A$ has $m$ elements and $n$ is a positive integer?
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Kenneth Rosen Edition 7th Exercise 2.1 Question 36 (Page No. 126)
How many different elements does $A \times B \times C$ have it $A$ has $m$ elemetns, $B$ has $n$ elements, and $C$ has $p$ elements?
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Kenneth Rosen Edition 7th Exercise 2.1 Question 35 (Page No. 126)
How many different elements does $A \times B$ have if $A$ has $m$ elements and $B$ has $n$ elements?
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Kenneth Rosen Edition 7th Exercise 2.1 Question 34 (Page No. 126)
Find $A^3$ if $A=\left \{ a \right \}$ $A= \left \{ 0,a \right \}$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 33 (Page No. 126)
Find $A^2$ if $A = \left \{ 0,1,3 \right \}$ $A = \left \{ 1,2,a,b \right \}$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 32 (Page No. 126)
Let $A = \left \{ a,b,c \right \}$, $B = \left \{ x,y \right \},$ and $C= \left \{ 0,1 \right \}$. Find $A \times B \times C$ $C \times B \times A$ $C \times A \times B$ $B \times B \times B$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 31 (Page No. 126)
Let $A$ be a set. Show that $ \phi \times A = A \times \phi = \phi$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 30 (Page No. 126)
Suppose that $A \times B = \phi$, where $A$ and $B$ are sets. What can you conclude?
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Kenneth Rosen Edition 7th Exercise 2.1 Question 29 (Page No. 126)
What is the Cartesian product $A \times B \times C$, where $A$ is the set of all airlines and $B$ and $C$ are both the set of all cities in the United States? Give an example of how this Cartesian product can be used.
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Kenneth Rosen Edition 7th Exercise 2.1 Question 28 (Page No. 126)
What is the Cartesian product $A \times B$, where $A$ is the set of courses offered by the mathematics department at a university and $B$ is the set of mathematics professors at this university? Give an example of how this Cartesian product can be used.
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Kenneth Rosen Edition 7th Exercise 2.1 Question 27 (Page No. 126)
Let $A = \left \{ a,b,c,d \right \}$ and $B= \left \{ y,z. \right \}$ Find $A \times B.$ $B \times A.$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 26 (Page No. 126)
Show that if $A \subseteq C$ and $B \subseteq D$, then $A \times B \subseteq C \times D$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 25 (Page No. 126)
Prove that $P(A) \subseteq P(B)$ if and only if $A \subseteq B.$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 24 (Page No. 126)
Determine whether each of these sets is the power set of a set, where $a$ and $b$ are distinct elements. $\phi$ $\left \{ \phi ,\left \{ a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ \phi ,a \right \} \right \}$ $\left \{ \phi ,\left \{ a \right \},\left \{ b \right \},\left \{ a,b \right \} \right \}$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 23 (Page No. 126)
How many elements does each of these sets have where $a$ and $b$ are distinct elements? $P (\left \{a,b, \left \{a,b \right \} \right \})$ $P\left \{ \phi, a, \left \{ a \right \},\left \{ \left \{ a \right \} \right \}\right \}$ $P(P(\phi ))$
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Kenneth Rosen Edition 7th Exercise 2.1 Question 22 (Page No. 126)
Can you conclude that $A=B$ if $A$ and $B$ are two sets with the same power set?
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Kenneth Rosen Edition 7th Exercise 2.1 Question 21 (Page No. 126)
Find the power set of each of these sets, where $a$ and $b$ are distinct elements {$a$} {$a,b$} {$\phi,$ {$\phi$}}
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Kenneth Rosen Edition 7th Exercise 2.1 Question 20 (Page No. 126)
What is the cardinality of each of these sets? $\phi$ {$\phi$} {$\phi$,{$\phi$}} {$\phi$, {$\phi$},{$\phi$, {$\phi$}}}
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