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Recent questions tagged discrete-mathematics

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Kenneth Rosen Edition 7 Exercise 6.1 Question 6 (Page No. 396)
There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?
There are four major auto routes from Boston to Detroit and six from Detroit to Los Angeles. How many major auto routes are there from Boston to Los Angeles via Detroit?
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634
Kenneth Rosen Edition 7 Exercise 6.1 Question 4 (Page No. 396)
A particular brand of shirt comes in $12$ colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made?
A particular brand of shirt comes in $12$ colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt a...
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636
Kenneth Rosen Edition 7 Exercise 6.1 Question 2 (Page No. 396)
An office building contains $27$ floors and has $37$ offices on each floor. How many offices are in the building?
An office building contains $27$ floors and has $37$ offices on each floor. How many offices are in the building?
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Kenneth Rosen Edition 7 Exercise 2.5 Question 39 (Page No. 177)
We say that a function is computable if there is a computer program that finds the values of this function. Use question $37$ and $38$ to show that there are functions that are not computable.
We say that a function is computable if there is a computer program that finds the values of this function. Use question $37$ and $38$ to show that there are functions th...
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648
Kenneth Rosen Edition 7 Exercise 2.5 Question 30 (Page No. 177)
Show that the set of real numbers that are solutions of quadratic equations $ax^{2} + bx + c = 0,$ where $a, b,$ and $c$ are integers, is countable.
Show that the set of real numbers that are solutions of quadratic equations $ax^{2} + bx + c = 0,$ where $a, b,$ and $c$ are integers, is countable.
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656
Kenneth Rosen Edition 7 Exercise 2.5 Question 22 (Page No. 177)
Suppose that $A$ is a countable set. Show that the set $B$ is also countable if there is an onto function $f$ from $A$ to $B.$
Suppose that $A$ is a countable set. Show that the set $B$ is also countable if there is an onto function $f$ from $A$ to $B.$
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Kenneth Rosen Edition 7 Exercise 2.5 Question 21 (Page No. 177)
Show that if $A, B,$ and $C$ are sets such that $\mid A\mid \leq \mid B \mid $ and $\mid B \mid \leq \mid C\mid ,$ then $\mid A\mid \leq \mid C \mid .$
Show that if $A, B,$ and $C$ are sets such that $\mid A\mid \leq \mid B \mid $ and $\mid B \mid \leq \mid C\mid ,$ then $\mid A\mid \leq \mid C \mid .$
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Kenneth Rosen Edition 7 Exercise 2.5 Question 19 (Page No. 177)
Show that if $A, B, C,$ and $D$ are sets with $ \mid A \mid = \mid B\mid $ and $\mid C\mid =\mid D\mid ,$ then $\mid A \times C \mid = \mid B \times D\mid .$
Show that if $A, B, C,$ and $D$ are sets with $ \mid A \mid = \mid B\mid $ and $\mid C\mid =\mid D\mid ,$ then $\mid A \times C \mid = \mid B \times D\mid .$
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