Logic/cs:where to look for examples?

[lizzyb]

Hi - I have homework like:

Question

Let A and B be finite sets of cardinalities m and n, respectively. You may assume m and n are positive integers but you may not assume any ordering of m and n. 1. How many relations are there from the set A to set B?

comments

I'm to arrive at a solution to this question logically, you know, show all the logic, but I'm not sure where to begin. I took a logic course about a year and a half ago and I admit I'm a bit rusty on it.

I purchased Velleman's How to Prove It and have been working through it in order to get up to speed; should I keep studying this book or look somewhere else?

 

[lizzyb]

I guess I answered my own question; there is plenty of stuff on the net plus I had a book from years back, Epp's Discrete Mathematics, 2nd; plus I reviewed the earthly-professor's commentary on the homework and I don't think he requires deductive reasoning with symbols (we may use prose).

 

[piercas]

I would suggest starting by breaking down the problem into smaller parts and then using logical reasoning to connect them. First, let's define what a relation is in this context. A relation from set A to set B is a subset of the Cartesian product A x B, which is the set of all ordered pairs (a,b) where a is an element of A and b is an element of B.

Next, we can consider the number of elements in A and B. Since we are not given any specific ordering, we can assume that A has m elements and B has n elements. This means that the Cartesian product A x B will have m x n elements.

Now, we can think about how many subsets of A x B can be considered as a relation. This can be visualized by thinking about all the possible ways to choose elements from A x B. Each element can either be included in the subset or not, giving us two options for each element. This means that the total number of subsets or relations is 2^(m x n).

In summary, the logical approach would be to define the problem, break it down into smaller parts, and then use logical reasoning to connect them and arrive at a solution. As for resources, it is always helpful to review concepts from a previous course, but you can also explore other textbooks or online resources for additional practice and examples. Good luck!