# Homework #10

Due in lecture, Thursday May 23. Please do the homework in a workbook.

# From the Text

Complete the following questions from the text:

• Section 8.1: 36, 44, 48, 56.
• Question 44: (a) and (b), those should be $$\ldots\in R$$.
• For 56, you can assume that $$R^n\circ R=R\circ R^n=R^{n+1}$$, which we haven't really proved.
• Section 8.3: 8, 14, 32.
• Section 8.4: 2, 10.

# Questions

1. Prove that taking the reflexive closure then symmetric closure of a relation is equivalent to taking the symmetric then reflexive closure. That is, it doesn't matter in which order we do the reflexive/symmetric closure operations; we get the same result either way.