Relations and Functions

Topics in this chapter

• Sets and Cartesian Products
• Relations and Equivalence Properties
• Function Domains and Ranges
• Types and Counting of Functions
• Function Composition and Inverses
• Real-Valued and Special Functions

Cheat sheet

Practice questions

1. Question 1Q-654944

   Let A = {1, 2, 3}, B = {a, b}, and R = {(1, a), (2, b), (3, a)}. Which statement is correct?

   1. A.R is not a function from A to B.
   2. B.The range of R is {a}.
   3. C.R is a function from A to B and its range is {a, b}.
   4. D.The range of R is {1, 2, 3}.
   See the answer and solution
2. Question 2Q-D8F718

   For the function f: R → R defined by f(x) = x², which statement is correct?

   1. A.f is one-one and onto.
   2. B.f is one-one but not onto.
   3. C.f is onto but not one-one.
   4. D.f is neither one-one nor onto.
   See the answer and solution
3. Question 3Q-18EC5C

   Define a relation R on the set of integers Z by a R b if and only if a − b is divisible by 3. Which statement is true?

   1. A.R is reflexive but neither symmetric nor transitive.
   2. B.R is symmetric but not reflexive.
   3. C.R is an equivalence relation on Z.
   4. D.R is neither reflexive nor symmetric.
   See the answer and solution
4. Question 4Q-80FF25

   Let f: R → R be defined by f(x) = (x − 1)² + 2. Find the range of f and state whether f is one-one.

   See the answer and solution
5. Question 5Q-16367D

   If A = {1, 2} and B = {a, b, c}, how many relations can be defined from A to B?

   1. A.6
   2. B.12
   3. C.32
   4. D.64
   See the answer and solution