Relations Let I be a set of sports teams: T= {Red Sox, Patriots, Spurs, Blackhawks, Giants, Celtics } We say that team x is "affiliated" with y if they won championships in the same year this century (note that some teams may have won more than one championship this century, but never more than one in a year). Let us define the relation "affiliated" (XAy) as a subset of the cartesian product Tx L That is: XAy = { (Red Sox, Red Sox), (Spurs, Spurs), (Giants, Giants), (Giants, Celtics), (Blackhawks, Red Sox) (Celtics, Giants), (Patriots, Spurs) (Red Sox, Patriots), (Patriots, Patriots), (Blackhawks, Blackhawks), (Celtics, Celtics), (Blackhawks, Patriots), (Spurs, Patriots) (Patriots, Red Sox) (Patriots, Blackhawks) (Red Sox, Blackhawks)} 1. Note that it may help to draw a diagram to answer the following questions! 2. Is the "affiliated" relation symmetric? Why or why not? Answer: 3. Is the "affiliated" relation transitive? Why or why not? Answer: 4. Is the "affiliated" relation reflexive? Why or why not? Answer: 5. Is the "affiliated" relation an equivalence relation? Why or why not? Answer:

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.