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1922
Kenneth Rosen Edition 7 Exercise 8.2 Question 5 (Page No. 524)
How many different messages can be transmitted in $n$ microseconds using the two signals described in question $19$ in Section $8.1?$
How many different messages can be transmitted in $n$ microseconds using the two signals described in question $19$ in Section $8.1?$
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1923
Kenneth Rosen Edition 7 Exercise 8.2 Question 42 (Page No. 526)
Show that if $a_{n} = a_{n-1} + a_{n-2}, a_{0} = s\:\text{and}\: a_{1} = t,$ where $s$ and $t$ are constants, then $a_{n} = sf_{n-1} + tf_{n}$ for all positive integers $n.$
Show that if $a_{n} = a_{n-1} + a_{n-2}, a_{0} = s\:\text{and}\: a_{1} = t,$ where $s$ and $t$ are constants, then $a_{n} = sf_{n-1} + tf_{n}$ for all positive integers $...
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1924
Kenneth Rosen Edition 7 Exercise 6.6 Question 7 (Page No. 438)
Use Algorithm $1$ to generate the $24$ permutations of the first four positive integers in lexicographic order.
Use Algorithm $1$ to generate the $24$ permutations of the first four positive integers in lexicographic order.
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1925
Kenneth Rosen Edition 7 Exercise 6.1 Question 26 (Page No. 397)
How many strings of four decimal digits do not contain the same digit twice? end with an even digit? have exactly three digits that are $9s?$
How many strings of four decimal digitsdo not contain the same digit twice?end with an even digit?have exactly three digits that are $9s?$
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1926
Kenneth Rosen Edition 7 Exercise 6.1 Question 70 (Page No. 398)
Use the product rule to show that there are $2^{2^{n}}$ different truth tables for propositions in $n$ variables.
Use the product rule to show that there are $2^{2^{n}}$ different truth tables for propositions in $n$ variables.
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1927
Kenneth Rosen Edition 7 Exercise 6.6 Question 11 (Page No. 438)
Show that Algorithm $3$ produces the next larger $r$-combination in lexicographic order after a given $r$-combination.
Show that Algorithm $3$ produces the next larger $r$-combination in lexicographic order after a given $r$-combination.
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1931
Kenneth Rosen Edition 7 Exercise 8.1 Question 9 (Page No. 511)
Find a recurrence relation for the number of bit strings of length n that do not contain three consecutive $0s.$ What are the initial conditions? How many bit strings of length seven do not contain three consecutive $0s?$
Find a recurrence relation for the number of bit strings of length n that do not contain three consecutive $0s.$ What are the initial conditions?How many bit strings of l...
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1938
Kenneth Rosen Edition 7 Exercise 6.4 Question 17 (Page No. 421)
Show that if $n$ and $k$ are integers with $1 \leq k \leq n,$ then $\binom{n}{k} \leq \frac{n^{k}}{2^{k−1}}.$
Show that if $n$ and $k$ are integers with $1 \leq k \leq n,$ then $\binom{n}{k} \leq \frac{n^{k}}{2^{k−1}}.$
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