(a) Explicitly check that [7] + [21] = [98] + [–5] in Z13- (b) Find another value of n such that [7] + [21] = [98] + [–5] makes sense in Zn. (c) Find a value of n such that [5] · [7] = [8] · [9] makes sense in Zn.

Answer the following:

Suppose L = {+, X, S, <, 0} is the first-order language of number theory (Peano's arithmetic). Write a term-calculation for S(n x (m + S(0)) + S(S(0 × n))). What is the value of this term when n = 2 and m = 3?

What is the least coefficient in the expansion of (x -1)7?

Write the following expression in terms of In x, In (x + 1), and In (x + 2). 1 7 In X+2 X +1 Choose the correct answer below. OA. 귀nx+ In (x+ 1)+ In (x+ 2) In (x + 1) + In (x+ 2) 7 In x + O B. In x-- In (x+ 1) – In (x + 2) 5 О В. OC. 7 In (x + 1) – In (x + 2) 1 Inx- 1 O D. In x+ In (x + 1) + 7 In (x + 2)

Multiply in Z9 [7][8]

Discrete math: Display addition and multiplication tables for Ζ8.

Write the expression in terms of In x, In (x +7), and In (x+ 8). In (x + 7)' (x + 8)² Choose the correct answer below. O A. In 1 = (In x-7 In (x +7) – 2 In (x + 8)) (x + 7) (x + 8)² B. In In x-7 In (x+7) +2 In (x + 8) (x+7) (x + 8)2 Vx O C. In 1. In x-7 In (x+ 7)-2 In (x+8) (x + 7)7 (x + 8)2 O D. In (In x - 7 In (x + 7) + 2 In (x + 8)) 2 (x + 7) (x + 8)2

28. In Example 9.7.5 it was shown that (a + b) = a* + 5a*b + 10a b² + 10a²b³ + 5ab* + b35. %3D Evaluate (a + b) by substituting the expression above into the equation (a + b) = (a + b)(a + b)³ and then multiplying out and combining like terms.