MTH302 - Counting Principles and Relations

1. Let A and B be two finite sets. If |A| = 10, |B| = 15, and |A ∩ B| = 5, what is |A ∪ B|?

a) 20 b) 25 c) 30 d) 35

2. How many integers between 1 and 100 are divisible by 2 or 3?

a) 50 b) 67 c) 75 d) 84

3. In a group of 13 people, what is the minimum number of people who share the same birth month?

a) 1 b) 2 c) 3 d) 4

4. If 25 objects are placed into 4 boxes, what is the minimum number of objects in the box with the most objects?

a) 6 b) 7 c) 8 d) 9

5. Which of the following is not a property of an equivalence relation?

a) Reflexive b) Symmetric c) Transitive d) Antisymmetric

6. Let R = {(1,1), (2,2), (3,3), (1,2)} be a relation on the set {1, 2, 3}. Which property does R satisfy?

a) Reflexive b) Symmetric c) Transitive d) Antisymmetric

7. Let R be a relation on a set A. If R is reflexive and transitive, what is R called?

a) Equivalence relation b) Partial order c) Total order d) Symmetric relation

8. How many people must be in a room to guarantee that at least two people have the same birthday (ignoring leap years)?

a) 365 b) 366 c) 367 d) 364

9. If 100 balls are placed into 10 boxes, what is the minimum number of balls in the box with the most balls?

a) 10 b) 11 c) 12 d) 13

10. Let R = {(1,2), (2,3), (1,3)} be a relation on the set {1, 2, 3}. Which property does R satisfy?

a) Reflexive b) Symmetric c) Transitive d) Antisymmetric

Counting Principles and Relations