A set is a well-defined collection of distinct objects, called elements or members.
For example:
- A = {1, 2, 3, 4}
- B = {apple, banana, orange}
In set A, the elements are 1, 2, 3 and 4.
Question 1: Given the set A = {1, 2, 3, 4, 5}, identify the type of set.
Solution:
The set A = {1, 2, 3, 4 ,5} is a Finite Set because it contains a definite number of elements (5 elements in this case).
Question 2: Let A = {1, 2, 3} and B = {3, 4, 5}. Find the union of sets A and B.
Solution:
The union of two sets A and B is the set of all elements that are in A, B, or both.
A ∪ B = {1, 2, 3, 4, 5} (Notice the duplicate element 3 is only counted once).
Question 3: Let A = {2, 4, 6, 8} and B = {1, 2, 3, 4}. Find the intersection of sets A and B.
Solution:
The intersection of two sets A and B is the set of all elements that are common to both sets.
A ∩ B = {2, 4}
Question 4: Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. Find the difference A − B.
Solution:
The difference A − B consists of elements that are in A but not in B.
A − B = {1, 2}
Question 5: Let U = {1, 2, 3, 4, 5, 6, 7} be the universal set, and A = {2, 4, 6}. Find the complement of A (denoted as Ac).
Solution:
The complement of set A, denoted Ac, consists of all the elements in the universal set U that are not in A.
Ac = U − A = {1, 3, 5, 7}
Practice Problems
Question 1: Given the set B = {a, e, i, o, u}, identify the type of set.
Question 2: Let X = {1, 2, 3, 4} and Y = {3, 4, 5, 6}. Find the union of sets X and Y.
Question 3: Let M = {2, 5, 7, 10} and N = {1, 5, 9, 10}. Find the intersection of sets M and N.
Question 4: Let P = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10}. Find the difference P − Q.
Question 5: Let U = {2, 4, 6, 8, 10, 12, 14} be the universal set, and S = {6, 8, 12}. Find the complement of S (denoted as Sc).
