Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where:
= {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the
following properties R has: reflexive, symmetric, anti-symmetric,
transitive? Justify your answer in each case?

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Ade and abc are similar. which best explains why the slope of the line between points a and d is the same as the slope between points a and b?

In which direction does the left side of the graph of this function point? f(x) = 3x3 - x2 + 4x - 2