(1) List the elements of ⋆ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. (2) Draw a digraph of ⋆ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Remember that a digraph just has one copy of each element! (3) Is ⋆ reflexive, antisymmetric, symmetric, and/or transitive? Explain your answer.
Please help me solve from question 4 to 10. Thank you.
For this Big Problem, we’re going to experiment with some unusual relations. The relation
⋆ means “this number written out in English has this many letters”. For example, 6 ⋆ 3
because the word “six” has 3 letters in it.
(1) List the elements of ⋆ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(2) Draw a digraph of ⋆ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Remember that a digraph just has
one copy of each element!
(3) Is ⋆ reflexive, antisymmetric, symmetric, and/or transitive? Explain your answer.
(4) Pick another language and let the relation ♡ mean “this number written out in [your
language] has this many letters”. List the elements of ♡ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(5) Draw a digraph of ♡ on {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(6) Is ♡ reflexive, antisymmetric, symmetric, and/or transitive? Explain your answer.
(7) Look at your digraph of ⋆ from question two. Imagine starting at 10 and following
the arrows as far as you can. Where do you end up?
(8) Look at your digraph of ⋆ from question two. Imagine starting at 7 and following
the arrows as far as you can. Where do you end up?
(9) What do you think happens for ⋆ no matter what number you begin with, if you
keep following the arrows?
(10) Now look at your digraph of ♡. Does the same thing happen? Why or why not?
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)