With respect to a universal set, which relation holds between a set and its complement?
Answer and explanation
Correct answer: वे परस्पर असंबद्ध होते हैं और उनका संघ सार्वत्रिक समुच्चय होता है।
For any set \(A\) defined inside a universal set \(U\), its complement \(A^c\) contains precisely the elements of U that are not in A. Thus no element can belong to both sets, so \(A\cap A^c=\varnothing\). At the same time, every element of U belongs to A or to its complement, so \(A\cup A^c=U\). Therefore option A states both correct properties.
Frequently asked questions
What is the correct answer to this question?
वे परस्पर असंबद्ध होते हैं और उनका संघ सार्वत्रिक समुच्चय होता है।
Why is this the correct answer?
For any set \(A\) defined inside a universal set \(U\), its complement \(A^c\) contains precisely the elements of U that are not in A. Thus no element can belong to both sets, so \(A\cap A^c=\varnothing\). At the same time, every element of U belongs to A or to its complement, so \(A\cup A^c=U\). Therefore option A states both correct properties.
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.
