MCQ WORKSHEET 1

 

1. Which of the following is a relation? a) A = {1,2,3,4} b) B = {x : x is a prime number} c) C = {(1,2), (2,4), (3,6)} d) D = {x : x is a fruit}

Answer: c) C = {(1,2), (2,4), (3,6)}

2. Which of the following is a reflexive relation? a) R = {(1,2), (2,3), (3,4)} b) S = {(1,1), (2,2), (3,3)} c) T = {(a,b), (b,c), (c,d)} d) U = {(x,y) : x + y = 0}

Answer: b) S = {(1,1), (2,2), (3,3)}

3. Which of the following is not a function? a) f(x) = x^2 b) g(x) = 2x - 1 c) h(x) = x + 1 if x is even, 2x if x is odd d) k(x) = {1,2,3}

Answer: d) k(x) = {1,2,3}

4. Which of the following is a one-to-one function? a) f(x) = 2x + 1 b) g(x) = x^2 c) h(x) = x + 3 d) k(x) = {1,2,3}

Answer: a) f(x) = 2x + 1

5. Which of the following is an equivalence relation? a) R = {(1,2), (2,3), (3,4)} b) S = {(1,1), (2,2), (3,3)} c) T = {(a,b), (b,c), (c,a)} d) U = {(x,y) : x + y = 0}

Answer: c) T = {(a,b), (b,c), (c,a)}

1. If a relation R on a set A is reflexive and transitive, then it is also: a. Symmetric b. Anti-symmetric c. Equivalence relation d. None of the above

2. Which of the following is not a type of function? a. One-to-one b. Many-to-one c. Onto d. Many-to-many

3. Which of the following statements is true about an onto function? a. It is also called a surjective function b. It is also called an injective function c. It has a unique inverse function d. It is not a type of function

4. If a function f(x) is defined on a set A, then the range of f(x) is: a. A b. The set of all real numbers c. The set of all values of f(x) d. The empty set

5. If a relation R on a set A is reflexive, symmetric, and transitive, then it is also: a. An equivalence relation b. A one-to-one function c. A onto function d. A many-to-one function

Answers:

1. c
2. d
3. a
4. c
5. a

MCQ Worksheet 1:

1. If a relation R is reflexive and symmetric, then it is also a. transitive b. anti-symmetric c. both a and b d. none of the above

2. If f(x) = x^2, then f^-1(x) = a. x^2 b. sqrt(x) c. 1/x^2 d. x/2

3. If a function is one-to-one, then it is also a. onto b. not onto c. reflexive d. symmetric

4. If a relation R is transitive and anti-symmetric, then it is also a. reflexive b. symmetric c. equivalence relation d. none of the above

5. If f(x) = 2x + 3 and g(x) = 5x - 1, then (f∘g)(x) = a. 10x + 17 b. 10x + 2 c. 7x + 2 d. 7x + 17

MCQ Worksheet 2:

1. If a relation R is symmetric and transitive, then it is also a. reflexive b. anti-symmetric c. equivalence relation d. none of the above

2. If a function is onto, then it is also a. one-to-one b. not one-to-one c. reflexive d. symmetric

3. If f(x) = x^3, then f^-1(x) = a. x^3 b. cube root of x c. 1/x^3 d. x/3

4. If a relation R is reflexive and anti-symmetric, then it is also a. symmetric b. transitive c. equivalence relation d. none of the above

5. If f(x) = 2x - 1 and g(x) = 3x + 2, then (g∘f)(x) = a. 6x + 1 b. 6x - 5 c. 5x - 1 d. 5x - 5