If U = {p, q, r, s, t, u, v, w}, A′ = {q, s, w}, and B′ = {p, s, u}, what is (A ∪ B)′?
Answer and explanation
Correct answer: {s}
Use De Morgan’s law, which states that (A ∪ B)′ = A′ ∩ B′. The given complements are A′ = {q, s, w} and B′ = {p, s, u}. Comparing the two lists, s is the only element appearing in both sets. Hence A′ ∩ B′ = {s}, and therefore (A ∪ B)′ = {s}. Option B is their union, not their intersection, while options C and D do not contain exactly the common elements.
Frequently asked questions
What is the correct answer to this question?
{s}
Why is this the correct answer?
Use De Morgan’s law, which states that (A ∪ B)′ = A′ ∩ B′. The given complements are A′ = {q, s, w} and B′ = {p, s, u}. Comparing the two lists, s is the only element appearing in both sets. Hence A′ ∩ B′ = {s}, and therefore (A ∪ B)′ = {s}. Option B is their union, not their intersection, while options C and D do not contain exactly the common elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
