Given any partial order P , we can form its sym metric closure P8 by taking the union of P and p - 1 . (a) Explain why P8 is reflexive and symmetric. (b) Given an example of a partial order P such that P8 is not an equivalence relation. (c) Give an example of such a P that also has the property from Problem 2.10.8. ( d) Prove that if P is a linear order, then P8 is an equivalence relation. ( e) Can you find an example of a P that is not a linear order, where P8 is an equivalence relation

Zahra was given two data sets, one without an outlier and one with an outlier. data without an outlier: 15, 19, 22, 26, 29 data with an outlier: 15, 19, 22, 26, 29, 81

Part one: measurements 1. measure your own height and arm span (from finger-tip to finger-tip) in inches. you will likely need some from a parent, guardian, or sibling to get accurate measurements. record your measurements on the "data record" document. use the "data record" to you complete part two of this project. name relationship to student x height in inches y arm span in inches archie dad 72 72 ginelle mom 65 66 sarah sister 64 65 meleah sister 66 3/4 67 rachel sister 53 1/2 53 emily auntie 66 1/2 66 hannah myself 66 1/2 69 part two: representation of data with plots 1. using graphing software of your choice, create a scatter plot of your data. predict the line of best fit, and sketch it on your graph. part three: the line of best fit include your scatter plot and the answers to the following questions in your word processing document 1. 1. which variable did you plot on the x-axis, and which variable did you plot on the y-axis? explain why you assigned the variables in that way. 2. write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. show all your work, including the points used to determine the slope and how the equation was determined. 3. what does the slope of the line represent within the context of your graph? what does the y-intercept represent? 5. use the line of best fit to you to describe the data correlation.

If 25% of y is 30, what is 60% of y?