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481
Kenneth Rosen Edition 7 Exercise 2.3 Question 14 (Page No. 153)
Determine whether $f: Z \times Z \rightarrow Z$ is onto if $f(m,n) = 2m-n.$ $f(m,n) = m^2-n^2.$ $f(m,n) = m+n+1.$ $f(m,n) = |m|-|n|.$ $f(m,n) = m^2-4.$
Determine whether $f: Z \times Z \rightarrow Z$ is onto if$f(m,n) = 2m-n.$$f(m,n) = m^2-n^2.$$f(m,n) = m+n+1.$$f(m,n) = |m|-|n|.$$f(m,n) = m^2-4.$
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482
Kenneth Rosen Edition 7 Exercise 2.3 Question 11 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is onto? $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$
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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483
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$$f(n) =\left \lceil n/2 \right \rceil$
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484
Kenneth Rosen Edition 7 Exercise 2.3 Question 12 (Page No. 153)
Determine whether each of these functions from $Z$ to $Z$ is one-to-one. $f(n) = n-1$ $f(n) =n^2+1$ $f(n)= n^3$ $f(n) =\left \lceil n/2 \right \rceil$
Determine whether each of these functions from $Z$ to $Z$ is one-to-one.$f(n) = n-1$$f(n) =n^2+1$$f(n)= n^3$$f(n) =\left \lceil n/2 \right \rceil$
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485
Kenneth Rosen Edition 7 Exercise 2.3 Question 10 (Page No. 153)
Determine whether each of these functions form $[a,b,c,d]$ to itself is one-to-one. $f(a)=b, f(b)=a,f(c)=c,f(d)=d$ $f(a)=b, f(b)=b,f(c)=d,f(d)=c$ $f(a)=d, f(b)=b,f(c)=c,f(d)=d$
Determine whether each of these functions form $[a,b,c,d]$ to itself is one-to-one.$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)...
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495
Kenneth Rosen Edition 7 Exercise 2.2 Question 37 (Page No. 137)
Show that if $A$ is a subset of a universal set $U$, then $A \oplus A = \phi.$ $A \oplus \phi = A.$ $A \oplus U = \sim A.$ $A \oplus \sim A= U.$
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.$$A \oplus \sim A= U.$
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500
Kenneth Rosen Edition 7 Exercise 2.2 Question 30 (Page No. 137)
Can you conclude that $A = B$ if $A,B,$ and $C$ are sets such that $A \cup C = B \cup C?$ $A \cap C = B \cap C?$ $A \cup C = B\cup C$ and $A \cap C = B \cap C?$
Can you conclude that $A = B$ if $A,B,$ and $C$ are sets such that$A \cup C = B \cup C?$$A \cap C = B \cap C?$$A \cup C = B\cup C$ and $A \cap C = B \cap C?$
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501
Kenneth Rosen Edition 7 Exercise 2.2 Question 29 (Page No. 136)
What can you say about the sets $A$ and $B$ if we know that $A \cup B = A?$ $A \cap B = A?$ $A- B = A?$ $A \cap B =B \cap A?$ $A –B = B-A?$
What can you say about the sets $A$ and $B$ if we know that$A \cup B = A?$$A \cap B = A?$$A- B = A?$$A \cap B =B \cap A?$$A –B = B-A?$
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502
Kenneth Rosen Edition 7 Exercise 2.2 Question 28 (Page No. 136)
Draw the Venn diagrams for each of these combinations of the sets $A,B,C,$ and $D.$ $(A \cap B) \cup (C \cap D)$ $ \sim A \cup \sim B \cup \sim C \cup \sim D$ $A -(B \cap C \cap D)$
Draw the Venn diagrams for each of these combinations of the sets $A,B,C,$ and $D.$$(A \cap B) \cup (C \cap D)$$ \sim A \cup \sim B \cup \sim C \cup \sim D$$A -(B \cap C ...
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503
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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504
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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507
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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508
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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509
Kenneth Rosen Edition 7 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 $A \cup (B \cup C)= (A \cup B) \cup C.$
Prove the first associative law from Table 1 by showing that if $A,B,$ and $C$ are sets, then $A \cup (B \cup C)= (A \cup B) \cup C.$
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