math 5

Discrete Mathematics

Readings Check section 5.3

Read Section 5.3, pages 260 ( 265.

Type in the answers below each question and email the completed document to me, or print out the document and fill it out by hand and email a scan or photo of it to me.

1) Why is the case of example 5.20 not an onto function?

2) Does a one(to(one function also have to be onto? If so then explain why. If not then give an example of a one(to(one function that is not onto.

3) Does an onto function also have to be one(to(one? If so then explain why. If not then give an example of an onto function that is not one(to(one..

4) Looking at example 5.23, if A = {w, x, y} then how many onto functions are there from A onto B? In other words, answer the question in the example when m = 3.

5) The blue box at the top of page 262 gives a formula for the number of onto functions from domain A onto range B. With |A| = m and |B| = n, what does this formula equal in terms of distributions of objects into containers? [be precise] [Hint: see the middle of page 262.]

6) If m = 10 and n = 5, explain in words what the formula in the box on page 263 calculates. [That is, the formula for Stirling numbers of the second kind.]

After submitting this form, go on to watch the videos, read the notes, and start the homework assignment for section 5.3. Ask any questions that arise at any point in the process. When the homework assignment is done, and you feel that you have a solid understanding of the homework and the section, then take the quiz for section 5.3.