Recall that we define [5 pts] zn = {[0],−1]} to be the set of congruence classes modulo n. also define the function fn : zn →zn, f(x) = x2. for example, z11 = {[0],[1],}, and f11([5]) = [3], since 52 = 25 ≡ 3 (mod 11). (a) create a table showing all input-output pairs for the function f11 : z11 →z11. (b) show that f11 is neither surjective nor injective. (c) show that fn is never injective for integer n ≥ 3. (hint: consider what happens to the congruence classes [1] and [n−1].)

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.