Relations and Functions

Let A = {1, 2, 3} and B = {4, 5}. How many relations are possible from A to B?

If f: R → R is defined by f(x) = 3x + 7, which of the following is true?

Consider the relation R on set A = {1,2,3} defined by R = {(1,1), (2,2), (3,3), (1,2), (2,3)}. Which property does R satisfy?

If a function f: R → R satisfies f(x + y) = f(x) + f(y) for all real x,y and f(1) = 4, find f(3).

Which of the following relations on set Z (integers) is an equivalence relation?

Let f: R → R be defined by f(x) = x². Which of the following statements is true?

If f: A → B and g: B → C are functions, which of the following is always true?

Find the number of onto functions from a set A with 3 elements to a set B with 2 elements.

Let R be a relation on set A = {1,2,3} defined by R = {(1,2), (2,3), (1,3)}. Which of the following is true?

If f: R → R is defined by f(x) = ax + b and is invertible, then the inverse function f⁻¹(x) is given by: