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

Which number line represents the solution set for the inequality - x 24?

Need now max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

What is the least common multiple for 6 and 8? what is the least common multiple for 4 and 12 ? what is the least common multiple for 11 and 12? what is the least common multiple for 3 and 6?