Functions / Sets / Finite Sets

Looking at some exercises in my discrete math book, I came across a few confusing problems.

1) For which sets A, B is it true that A x B = B x A?

2) If there are 2187 functions f: A → B and |B| = 3, what is |A|?

3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that

a) f is neither one-to-one nor onto.

Re: Functions / Sets / Finite Sets

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Originally Posted by

**rhymin** Looking at some exercises in my discrete math book, I came across a few confusing problems.

1) For which sets A, B is it true that A x B = B x A?

2) If there are 2187 functions f: A → B and |B| = 3, what is |A|?

3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that

a) f is neither one-to-one nor onto.

2) $\displaystyle |B|^{|A|}$ is the number of functions from A to B.

Re: Functions / Sets / Finite Sets

Quote:

Originally Posted by

**rhymin** Looking at some exercises in my discrete math book, I came across a few confusing problems.

1) For which sets A, B is it true that A x B = B x A?

2) If there are 2187 functions f: A → B and |B| = 3, what is |A|?

3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that

a) f is neither one-to-one nor onto.

What are you finding confusing? Do you understand all the terminology and notation? Often that is half the problem...

Re: Functions / Sets / Finite Sets

Plato, thank you.

And, Ant, yes that is the first part of the problem for me.

Re: Functions / Sets / Finite Sets

well, feel free to ask if you want any clarification. that might be more helpful than just telling you the answers!

Re: Functions / Sets / Finite Sets

Usually when I see how to begin, or some of the work, it goes a long way in helping me find the answer.

In some cases though, seeing the answer first helps me to see how it was actually solved.

Re: Functions / Sets / Finite Sets

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**rhymin** 1) For which sets A, B is it true that A x B = B x A?

Consider the following cases.

(1) A is empty or B is empty;

(2) A and B are singletons containing the same element;

(3) There exist x ≠ y such that x ∈ A and y ∈ B.

Are these cases exhaustive? What can be said about A x B and B x A in each case?

Quote:

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**rhymin** 3) Give an example of finite sets A and B with |A|, |B| ≥ 4 and a function f: A→B such that

a) f is neither one-to-one nor onto.

Surely this is easy. Think of a group of boys and a group of girls and imagine who loves whom so that there is no chance of a happy outcome :( As a famous Russian song goes, "Because there are nine boys for every ten girls according to statistics".

Re: Functions / Sets / Finite Sets

Sorry, I'm lost. I don't know where to begin.

Re: Functions / Sets / Finite Sets

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**rhymin** Sorry, I'm lost. I don't know where to begin.

You best go have a sit-down face-to-face talk with your instructor.

Re: Functions / Sets / Finite Sets

I'm not in a class yet. I guess I should explain this at the beginning of each post.

I just started going back to college and will be taking a discrete math course. I haven't been in a math class for several years (probably 8) and I knew I would struggle if I didn't practice before. My friend is the same major as me (information technology) and had a discrete math book. I am looking at the exercises from each section to try and learn as much as I can before my class.

Re: Functions / Sets / Finite Sets

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**rhymin** I'm not in a class yet. I guess I should explain this at the beginning of each post.

I just started going back to college and will be taking a discrete math course. I haven't been in a math class for several years (probably 8) and I knew I would struggle if I didn't practice before. My friend is the same major as me (information technology) and had a discrete math book. I am looking at the exercises from each section to try and learn as much as I can before my class.

In that case start at page 1 and read carefully.

Use paper and pencil and copy out any and all examples worked out in that textbook.

Re: Functions / Sets / Finite Sets

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**rhymin** I am looking at the exercises from each section to try and learn as much as I can before my class.

But have you read the sections themselves before the exercises? Have you understood solved examples treated in the text? Do you know the definition of an ordered pair and Cartesian product?

I would like to say, though, that reading a course text before the beginning of the course is a very good idea, in my opinion, provided you have enough motivation to go through and understand at least some of the material.

Re: Functions / Sets / Finite Sets

Yeah, unfortunately though, I do kind of pick and choose exercises and do not read everything in each section simply because I just don't have enough time for it. I have been reading probably 30min to 1 hour a day. The one good thing though is this forum, I can check it real quick at work or at home throughout most of the day and add quick replies, which is very helpful so far.

Re: Functions / Sets / Finite Sets

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**Plato** In that case start at page 1 and read carefully.

Use paper and pencil and copy out any and all examples worked out in that textbook.

I started out doing this, but realized it takes way too much time which unfortunately, I do not have. I've been kind of picking and choosing exercises that look confusing, and then going back and looking at similar examples...or trying to find similar examples.

Usually what I post on here are exercises that I couldn't figure out because the examples weren't close enough, or I just don't know enough about the subjects to figure them out myself.

Re: Functions / Sets / Finite Sets

Honestly, I think for these 3 particular problems, it would go a long way just to see the answers, and then I can kind of work backwards to figure out how they were done.

I guess it just depends what type of problem it is, but I don't like to do this for all problems. There is just a sense of satisfaction of figuring out the answer sometimes, but for these I'm having more than usual trouble.