Practice Problems on Complement of a Set

Following are some practice questions that explain the concept of Complement of a Set:

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

Solution:

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

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

Solution:

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}.

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

Solution:

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}.

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

Solution:

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}.

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

Solution:

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}.

Problem 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}.

Solution:

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}.

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

Solution:

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}.

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

Solution:

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}.

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

Solution:

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}.

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

Solution:

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}.