Consider the functions f : A → B, g : B → A and h : B → A such that if gf = 1A and fh = 1B. Prove (a) f is a 1-1 correspondence A ∼ B. (b) f1A = f and 1Bf = f.

Determine the domain and range of the relation R defined byR = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}.

Consider a function f defined from the interval [4, 7] to the interval [4, 7]. Which of the 7 following is a possible value of f(x) dæ? Select one: Ο Α 16 ОВ. 28 O C. 4 O D. 49 ОЕ7

Which of the following relation is a function? a) Z={(1,4), (2,3), (3,2). (2,4), (1,4), (1,5 )} b) s={(- 2,1) (- 1,2) (1,2) (2,1) (3,4). (5,7)} c) A={1,3). (2. – 5 ). (1.5). (- 3,1) (- 2,–2).} d) M = {(2.1) (5.1) (8,1) (11.1). (1.1) (2.5)}

Let A = {a, b, c, d, e}, B = {1, 2, 3, 4, 5} and let f : A → B, f(a) = 5, f(b) = 2, f(c) = 3, f(d) = 1, f(e) = 4. Decide, whether f is invertible and, if yes, determine its inverse function