Suppose A = {-4,-3,–2,–1,0,1,2,3,4} and R is defined on A by aRb a² - b² is divisible by 4. Prove that R is equivalence relation on A. Find all distinct equivalence classes of A with respect to R.

The table below contains the periodontal status of individuals and their sex. Periodontal status refers to gum disease where individuals are classified as either Healthy, have Gingivitis, or have Periodontal Disease (Perio). Female Male Total Healthy 2108 1124 3232 Gingivitis 1582 937 2519 Perio 873 931 1804 Total 4563 2992 7555 Find Pr{Female or Gingivitis). If necessary, round your answer to 3 places after the decimal.

How many ways can you arrange the letters of ANTIDIFFERENTIATE if it must end with an E, and the R  and the D must be adjacent to each other (RD or DR) ?

3] Provide an example of a qualitative variable. You may not use an example provided in th notes.