1. (Warming Up) a. Let the function f : N - N be defined by f(n) = 3 . n i. Give Dom(f). Codom(f ) and Im(f). ii. Is f one -to-one ? Is it onto ? iii. Does f-1 exist ? iv. Compute (f . f)(1) and both f((0, 1, 2, 3)) and f *({0, 1, 2,3}) b. For the two matrices calculate A , A +B and B2 c. Consider the following (binary ) relations on S = {0,1,2,3 }: . (m,n)ER, if m + n = 4. . (m,n)ER2 if m - nes. . (m,n) e Rg if m = max {n, 1}. Hint : max {x,y} means the larger of the two numbers x and y. i. Write each of the relations as a set of ordered pairs. ii. Specify which of the properties (R), (AR), (S), (AS) and (T) the relations satisfy. iii. Write R2- as a set of ordered pairs and give R2 ({0,1 }) and R2- ({0,1}). 2. (Functions ) Let E = (0, 1 ). Consider the functions f, g : 2* - E* and h : E* x E" - >* given by . f(@) = 160 . g(@) = 00 . h(v. @) = vov Compute the following function values a. (f . g)(01) b. (g . f)(01)