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Kenneth Rosen Edition 7 Exercise 2.3 Question 15 (Page No. 153)
Determine whether the function $f: Z \times Z \rightarrow Z$ is onto if $f(m,n) = m+n$ $f(m,n) = m^2+n^2.$ $f(m,n) = m.$ $f(m,n) = |n|.$ $f(m,n) = m-n.$
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) = m-n.$
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Kenneth Rosen Edition 7 Exercise 2.3 Question 13 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is onto?? $f(n) = n-1$ $f(n) =n^2+1$ $f(n)= n^3$ $f(n) =\left \lceil n/2 \right \rceil$
Determine whether each of these functions from $Z$ to $Z$ is onto??$f(n) = n-1$$f(n) =n^2+1$$f(n)= n^3$$f(n) =\left \lceil n/2 \right \rceil$
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Kenneth Rosen Edition 7 Exercise 1.7 Question 36 (Page No. 91)
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.
Show that the propositions $p1,p2,p3$, and $p4$can be shown to be equivalent by showing that $p1 \leftrightarrow p4,p2 \leftrightarrow p3$, and $p1 \leftrightarrow p3$.
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Kenneth Rosen Edition 7 Exercise 2.2 Question 27 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,$ and $C$. $A \cap (B-C)$ $(A \cap B) \cup (A \cap C)$ $(A \cap \sim B) \cup (A \cap \sim C)$
Draw the Venn diagrams for each of these combinations of the sets $A,B,$ and $C$.$A \cap (B-C)$$(A \cap B) \cup (A \cap C)$$(A \cap \sim B) \cup (A \cap \sim C)$
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Rosen chapter 5.5 question 50
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
How many ways are there to distribute 5 distinguishable objects into three indistinguishable boxes?
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Kenneth Rosen Edition 7 Exercise 2.1 Question 43 (Page No. 126)
Find the truth set of each of these predicates where the domain is the set of integers. $P(x) : x^2<3$ $Q(x) : x^2 >x$ $R(x): 2x+1 = 0$
Find the truth set of each of these predicates where the domain is the set of integers.$P(x) : x^2<3$$Q(x) : x^2 >x$$R(x): 2x+1 = 0$
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Kenneth Rosen Edition 7 Exercise 2.2 Question 26 (Page No. 136)
Draw the Venn diagrams for each of these combination sof the sets $A,B,$ and $C$. $A \cap (B \cup C)$ $\sim A \cap \sim B \cap \sim C$ $(A-B) \cup (A-C) \cup (B-C)$
Draw the Venn diagrams for each of these combination sof the sets $A,B,$ and $C$.$A \cap (B \cup C)$$\sim A \cap \sim B \cap \sim C$$(A-B) \cup (A-C) \cup (B-C)$
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Kenneth Rosen Edition 7 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 $A \cup(B \cap C) = (A \cup B) \cap (A \cup C).$
Prove the first distributive law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup(B \cap C) = (A \cup B) \cap (A \cup C).$
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Kenneth Rosen Edition 7 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?
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?
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Kenneth Rosen Edition 7 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 $A \cup (B \cap C) = (A \cap B) \cap C.$
Prove the second associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cap C) = (A \cap B) \cap C.$
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