Practice Problems on Complement of a Set (original) (raw)

Last Updated : 1 Oct, 2025

**Learning the concept of complements in set theory is essential in mathematics. It allows us to analyze and manipulate sets in various ways, leading to valuable insights and solutions to different mathematical problems. And solving Practice Problems on the complement of a set is the best way to learn it.

**Solved Practice Problems on the Complement of a Set

**Question 1: Find the complement of the set A = {1, 2, 3, 4, 5} within the universal set U = {1, 2, 3, 4, 5}.

Since set A already includes all elements of universal set U, its complement is an empty set {}.

**Question 2: Find the complement of the set B = {a, b, c} within the universal set U = {a, b, c, d, e}.

Complement of set B within the universal set U consists of all elements in U that are not in B. Therefore, the complement of B is {d, e}.

**Question 3: Find the complement of the set C = {red, blue} within the universal set U = {red, blue, green, yellow}.

Complement of set C within the universal set U consists of all elements in U that are not in C. Therefore, the complement of C is {green, yellow}.

**Question 4: Find the complement of the set D = {0, 1, 2, 3} within the universal set U = {0, 1, 2, 3, 4, 5}.

Complement of set D within the universal set U consists of all elements in U that are not in D. Therefore, the complement of D is {4, 5}.

**Question 5: Find the complement of the set E = {cat, dog} within the universal set U = {cat, dog, bird, fish}.

Complement of set E within the universal set U consists of all elements in U that are not in E. Therefore, the complement of E is {bird, fish}.

**Question 6: Find the complement of the set F = {5, 10, 15} within the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.

Complement of set F within the universal set U consists of all elements in U that are not in F. Therefore, the complement of F is {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14}.

**Question 7: Find the complement of the set G = {x, y, z} within the universal set U = {w, x, y, z}.

Complement of set G within the universal set U consists of all elements in U that are not in G. Therefore, the complement of G is {w}.

**Question 8: Find the complement of the set H = {apple, banana} within the universal set U = {apple, banana, orange, pear}.

Complement of set H within the universal set U consists of all elements in U that are not in H. Therefore, the complement of H is {orange, pear}.

**Question 9: Find the complement of the set I = {100, 200, 300} within the universal set U = {0, 100, 200, 300, 400, 500}.

Complement of set I within the universal set U consists of all elements in U that are not in I. Therefore, the complement of I is {0, 400, 500}.

**Question 10: Find the complement of the set J = {Monday, Tuesday, Wednesday} within the universal set U = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}.

Complement of set J within the universal set U consists of all elements in U that are not in J. Therefore, the complement of J is {Thursday, Friday, Saturday, Sunday}.

**Unsolved Practice Problems on Complement of a Set

Q1. What is the complement of the set A = {1, 2, 3, 4} within the universal set U = {1, 2, 3, 4, 5, 6, 7}?

Q2. What is the complement of the set B = {a, b, c, d} within the universal set U = {a, b, c, d, e, f, g}?

Q3. What is the complement of the set C = {red, blue, green} within the universal set U = {red, blue, green, yellow, orange}?

Q4. What is the complement of the set D = {0, 1, 2} within the universal set U = {0, 1, 2, 3, 4, 5}?

Q5. What is the complement of the set E = {cat, dog, fish} within the universal set U = {cat, dog, bird, fish, rabbit}?

Q6. What is the complement of the set F = {5, 10, 15, 20} within the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}?

Q7. What is the complement of the set G = {x, y, z, w} within the universal set U = {w, x, y, z, a, b, c, d}?

Q8. What is the complement of the set H = {apple, banana, orange} within the universal set U = {apple, banana, orange, pear, mango}?

Q9. What is the complement of the set I = {100, 200, 300, 400} within the universal set U = {0, 100, 200, 300, 400, 500, 600, 700}?

Q10. What is the complement of the set J = {Monday, Tuesday, Wednesday, Thursday} within the universal set U = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}?