Math in modern world include solution please thanks

c) G E Z, defined * by a * b = a + ab - b for all set a, be Z. Explanation: d) G E R, defined * by a * b = va - b for all set a, be R. Explanation: D. Let S = Z* as define * on S by a * b = a + b + 1. Show the associativity and the commutativety of S in a binary operation. Determine also the identity if there is. E. Let A = Z- (0) and let S = (fi, f2, f3, f4, fs, fo] be the set of functions as A defined as follows: fi (x) = x FA (x) = = f2 (x ) = - fs (x) = fa (x) = *-1 f6 = 1 - xDirections. Do as indicated. A. Define a relation C from R to R as follows: For any (x,y) ER x R, (x,y) E C meaning that x2 + y? = 1. a. Is (1,0) E C? Is (0,0) E C? Is -2 C O? Is 0 C (-1)? b. What are the domain and the co-domain of C? B. If f(x) = 2x2 and g(x) = 3x + 1, evaluate the following: a. (f+ g)(x) b) (f . g)(x) c) (E) ( x ) d) (go f) (x) C. Tell whether the following is a binary operation or not. a) G E Z, defined * by a * b = a - b' for all set a, be Z. Explanation: b) G E N, defined * by a * b = 2 + 3ab for all set a, be N. Explanation