Question

Describe the following set in words: A∪(B′∩C′)

Answer 1

The set A∪(B′∩C′) is described as the union of set A and the intersection of the complements of sets B and C. This means combining all the elements from set A with the elements that are common to the complements of sets B and C.

Step-by-step explanation:

The set A∪(B′∩C′) is described as the union of set A and the intersection of the complements of sets B and C. To understand this, let's break it down:

1. First, find the complement of sets B and C. This means finding all the elements that are not in sets B and C.
2. Next, find the intersection of the complements. This means finding the elements that are common to the complements of sets B and C.
3. Finally, take the union of set A with the intersection of the complements. This means combining all the elements from set A with the elements that are common to the complements of sets B and C.

For example, if set A = {1, 2} and sets B and C have complements B' = {2, 3, 4} and C' = {4, 5}, respectively, then A∪(B′∩C′) would be {1, 2}∪({2, 3, 4}∩{4, 5}) = {1, 2}∪{} = {1, 2}. So, the described set is just set A.