If A ⊆ B ⊆ C ⊆ U, which relation is correct for their complements?
Answer and explanation
Correct answer: Cᶜ ⊆ Bᶜ ⊆ Aᶜ
Taking the complement reverses the direction of set inclusion. Since A ⊆ B, every element outside B is also outside A, so Bᶜ ⊆ Aᶜ. Similarly, B ⊆ C gives Cᶜ ⊆ Bᶜ. Combining these results gives Cᶜ ⊆ Bᶜ ⊆ Aᶜ. Therefore, option A is correct. Equality is not necessary, and the intersection of two complements cannot generally be the whole universal set.
Frequently asked questions
What is the correct answer to this question?
Cᶜ ⊆ Bᶜ ⊆ Aᶜ
Why is this the correct answer?
Taking the complement reverses the direction of set inclusion. Since A ⊆ B, every element outside B is also outside A, so Bᶜ ⊆ Aᶜ. Similarly, B ⊆ C gives Cᶜ ⊆ Bᶜ. Combining these results gives Cᶜ ⊆ Bᶜ ⊆ Aᶜ. Therefore, option A is correct. Equality is not necessary, and the intersection of two complements cannot generally be the whole universal set.
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.
