1. What is the cardinality of the set {1, 2, 3, 4, 5}?

a) 4 b) 5 c) 6 d) 0
2. Which of the following is a subset of {1, 2, 3}?
a) {1, 4} b) {1, 2} c) {4, 5} d) {1, 3, 4}

d) ∅
3. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is:
a) {1, 2} b) {3} c) {1, 2, 3, 4, 5}
4. The power set of {a, b} contains how many elements?
a) 1 b) 2 c) 4 d) 8

d) ∅
5. If U = {1, 2, 3, 4, 5} and A = {1, 2}, then A' is:
a) {1, 2, 3, 4, 5} b) {3, 4, 5} c) {1, 2}
6. Which of the following is not an empty set?
a) {x | x is an odd b) {x | x is a prime c) {x | x is a positive d) {0}
number divisible number less than integer less than 1}
by 2} 2}
7. The union of A = {1, 2, 3} and B = {3, 4, 5} is:

8. For any set A, A ∪ ∅ equals:

a) {3} b) {1, 2, 3, 4, 5} c) {1, 2} d) {1, 2, 4, 5}

a) A b) ∅ c) U d) None of these
9. If A = {1, 2, 3} and B = {a, b}, then A × B contains how many elements?
a) 2 b) 3 c) 5 d) 6
10. Which of the following is a universal set for the set of even numbers?
a) {1, 2, 3, 4, 5} b) {x | x is a natural c) {x | x is a real d) {x | x is a rational
number} number} number}
11. Which of the following is an example of a finite set?
a) {x | x is a positive b) {x | x is a prime c) {x | x is a real d) {x | x is an
integer less than number} number} irrational number}
10}

d) ∅
12. If A and B are disjoint sets, then A ∩ B equals:
a) A b) B c) U

b) ∅
13. The complement of the universal set U is:
a) U c) None of these d) A

a) (A ∪ B) ∩ (A ∩ B) b) (A ∪ B) – (A ∩ B)
14. The symmetric difference of A and B is defined as:
c) (A ∩ B) d) None of these
15. If A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}, then A – B is:
a) {1, 2, 3, 4, 5} b) {6, 7} c) {1, 2} d) {3, 4, 5}
16. Which of the following is an infinite set?
a) {1, 2, 3, ..., 100} b) {x | x is an integer c) {a, b, c} d) {0}
greater than 0}
17. If |A| = 3 and |B| = 2, then |A × B| equals:
a) 6 b) 5 c) 3 d) 8

a) ∅
18. The subset of every set is:

19. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∪ B contains how many elements?
b) U c) The set itself d) Both (a) and (c)

a) 4 b) 6 c) 8 d) 10

a) A ∪ A = A b) A ∩ A = ∅ c) A ∩ B = A ∪ B
20. Which of the following is true for all sets A and B?
d) None of these
21. If f(x) = x², what is f(3)?
a) 6 b) 9 c) 3 d) 0
22. A function f: A → B is called one-to-one if:
a) Every element in b) No two elements c) All elements in A d) None of the
 B is mapped to in A map to the map to all above
exactly one same element in B elements in B
element in A
23. The range of the function f(x) = sin(x) is:
a) (-∞, ∞) b) [-1, 1] c) [0, 1] d) [1, ∞)
24. Which of the following is an example of a subjective function?
a) f(x) = x + 1, where b) f(x) = x², where f: c) f(x) = sin(x), where d) None of these
f: R → R R→R f: R → [-1, 1]
25. The domain of the function f(x) = 1/x is:
a) R b) R – {0} c) {0} d) None of these
26. If f(x) = x³, then f(-2) is:

27. If f(x) = 2x + 1 and g(x) = x², then (f ∘ g)(x) is:

a) 8 b) -8 c) 4 d) -4

a) 2x² + 1 b) x² + 1 c) 2x + 1 d) None of these

28. The inverse of the function f(x) = 2x + 3 is:
a) (x - 3)/2 b) x/2 + 3 c) 2x - 3 d) None of these
29. If f(x) = |x|, then f(-5) is:
a) -5 b) 5 c) 0 d) None of these
30. The function f(x) = x² is:
a) One-to-one but b) Onto but not one- c) Neither one-to- d) Both one-to-one
not onto to-one one nor onto and onto
31. The graph of the function f(x) = x is:

32. If f(x) = x² and g(x) = x + 2, then (g ∘ f)(x) is:

a) A straight line b) A parabola c) A circle d) None of these

33. If f(x) = 2x and g(x) = 3x, then (f ∘ g)(x) is:

a) x² + 2 b) (x + 2)² c) x² + x + 2 d) None of these

a) 6x b) 2x c) 3x d) None of these
34. A constant function is:
a) One-to-one but b) Onto but not one- c) Both one-to-one d) Neither one-to-
not onto to-one and onto one nor onto
35. If f: R → R is defined by f(x) = x + 2, then f is:
a) One-to-one b) Onto c) Both one-to-one d) Neither one-to-
and onto one nor onto
36. If f(x) = x², what is the domain of f?
a) [-1, 1] b) R c) [0, ∞) d) None of these
37. If f(x) = sin(x), then f is:
a) One-to-one b) Onto c) Periodic d) None of these
38. The domain of f(x) = √x is:

39. The range of f(x) = x² for x ∈ R is:

a) [-1, ∞) b) [0, ∞) c) R d) None of these

a) [-∞, ∞) b) [0, ∞) c) (-∞, ∞) d) None of these

40. If f(x) = log(x), then the domain of f is:
a) R b) R+ c) R – {0} d) None of these