If 3 ∈ U and 3 ∉ A, which conclusion is correct?
Answer and explanation
Correct answer: 3 ∈ Aᶜ
For a set A defined within the universal set U, an element belongs to Aᶜ precisely when it belongs to U but does not belong to A. The question states both conditions for the element 3: 3 is in U and 3 is not in A. Hence 3 must belong to Aᶜ. It cannot belong to A, and it cannot belong to A ∩ Aᶜ because the latter is empty.
Frequently asked questions
What is the correct answer to this question?
3 ∈ Aᶜ
Why is this the correct answer?
For a set A defined within the universal set U, an element belongs to Aᶜ precisely when it belongs to U but does not belong to A. The question states both conditions for the element 3: 3 is in U and 3 is not in A. Hence 3 must belong to Aᶜ. It cannot belong to A, and it cannot belong to A ∩ Aᶜ because the latter is empty.
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.
