Question

Вопрос от 1 курса техникума. Дано: A={0,1,2,3,4,5,6} B={1,2,3,6,8} C={-1,0,3,4,7,8} Найти: A∪B; A∩B∩C; (A∪B)∩C; A∪(B∩C) P.S. Это одно задание, а не несколько.

Answer 1

A={0,1,2,3,4,5,6}
B={1,2,3,6,8}
C={-1,0,3,4,7,8}

Найти:
A∪B={0,1,2,3,4,5,6,8}
A∩B∩C={3}
(A∪B)∩C={0,3,4,8}
A∪(B∩C)={3}

Answer 2

Union, Intersection, and Complement of Sets

Let's solve the given problem step by step.

Finding A∪B (Union of A and B)

The union of two sets A and B, denoted as A∪B, is the set of all elements that are in A, in B, or in both A and B.

Given: A = {0, 1, 2, 3, 4, 5, 6} B = {1, 2, 3, 6, 8}

The union of sets A and B (A∪B) is the set of all unique elements from both sets.

A∪B = {0, 1, 2, 3, 4, 5, 6, 8} [[1]]

Finding A∩B∩C (Intersection of A, B, and C)

The intersection of multiple sets is the set of elements that are common to all of the sets.

Given: A = {0, 1, 2, 3, 4, 5, 6} B = {1, 2, 3, 6, 8} C = {-1, 0, 3, 4, 7, 8}

The intersection of sets A, B, and C (A∩B∩C) is the set of elements that are present in all three sets.

A∩B∩C = {3} [[2]]

Finding (A∪B)∩C (Intersection of A∪B and C)

First, we find the union of sets A and B (A∪B), and then we find the intersection of the resulting union with set C.

A∪B = {0, 1, 2, 3, 4, 5, 6, 8} C = {-1, 0, 3, 4, 7, 8}

A∪B∩C = {0, 3, 4, 8} [[3]]

Finding A∪(B∩C) (Union of A and the Intersection of B and C)

First, we find the intersection of sets B and C (B∩C), and then we find the union of set A with the resulting intersection.

B∩C = {3, 8} A = {0, 1, 2, 3, 4, 5, 6}

A∪(B∩C) = {0, 1, 2, 3, 4, 5, 6, 8} [[4]]

Conclusion

- A∪B = {0, 1, 2, 3, 4, 5, 6, 8} - A∩B∩C = {3} - (A∪B)∩C = {0, 3, 4, 8} - A∪(B∩C) = {0, 1, 2, 3, 4, 5, 6, 8}