If U is the set of students, A is the set of students studying Mathematics, and B is the set of students studying Physics, what does A'∩B' represent?
Answer and explanation
Correct answer: Students studying neither subject
A' consists of students who are not in A, so they do not study Mathematics. Similarly, B' consists of students who do not study Physics. Their intersection A'∩B' contains students satisfying both conditions simultaneously: they study neither Mathematics nor Physics. By De Morgan's law, A'∩B'=(A∪B)', which confirms that these are students outside the group studying at least one of the two subjects.
Frequently asked questions
What is the correct answer to this question?
Students studying neither subject
Why is this the correct answer?
A' consists of students who are not in A, so they do not study Mathematics. Similarly, B' consists of students who do not study Physics. Their intersection A'∩B' contains students satisfying both conditions simultaneously: they study neither Mathematics nor Physics. By De Morgan's law, A'∩B'=(A∪B)', which confirms that these are students outside the group studying at least one of the two subjects.
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.
