Register
Filter

Hot questions in Discrete Mathematics

0 votes
0 answers
1721
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.
User Avatar
0 votes
0 answers
1722
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 $9s?$
User Avatar
0 votes
0 answers
1723
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.
User Avatar
0 votes
0 answers
1724
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.
User Avatar
0 votes
0 answers
1728
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...
User Avatar
1 votes
0 answers
1735
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 $\binom{n}{k} \leq \frac{n^{k}}{2^{k−1}}.$
User Avatar
0 votes
0 answers
1738
Kenneth Rosen Edition 7 Exercise 6.5 Question 45 (Page No. 433)
How many ways can n books be placed on k distinguishable shelves if the books are indistinguishable copies of the same title? if no two books are the same, and the positions of the books on the shelves matter?
How many ways can n books be placed on k distinguishable shelvesif the books are indistinguishable copies of the same title?if no two books are the same, and the position...
User Avatar
0 votes
1 answer
1740
Kenneth Rosen Edition 7 Exercise 2.3 Question 40 (Page No. 154)
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that $f(S \cup T) = f(S) \cup f(T)$ $f(S \cap T) = f(S) \cap f(T)$
Let $f$ be a function from the set $A$ to the set $B$. Let $S$ adn$T$ be subsets of $A$ .Show that$f(S \cup T) = f(S) \cup f(T)$$f(S \cap T) = f(S) \cap f(T)$
User Avatar
Page: