Let σ Sn, and suppose that σ is written as a product of disjoint cycles. Show that σ is even if and only if the number of cycles of even length is even. Show that σ is odd if and only if the number cycles of even lengthis odd.

Solve the problem. a student earned grades of c, a, b, and a in four different courses. those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. the grading system assigns quality points to letter grades as follows: a = 4, b = 3, c = 2, d = 1, and f = 0. compute the grade point average (gpa) and round the result to two decimal places. 3.40 3.50 8.75 2.18