2. for each below, write as a product of disjoint cycles. determine if the permutation is even or odd, and find its order. (4 points) (a) (1243)(3521) (b) (12)(134) (152)

The diameter of a circular chip is doubled to use in a new board game. the area of the new chip will be

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?

How do the number line graphs of the solutions sets of -23 > x and x-23 differ?