Which set is always present in the power set of every set?
Answer and explanation
Correct answer: The empty set ∅
The empty set ∅ is a subset of every set because it has no elements that could violate the requirement for being a subset. Since a power set consists of all subsets of the original set, ∅ must occur in the power set of every set, including the empty set itself. The universal set or singleton sets are not guaranteed to be subsets of every possible set. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
The empty set ∅
Why is this the correct answer?
The empty set ∅ is a subset of every set because it has no elements that could violate the requirement for being a subset. Since a power set consists of all subsets of the original set, ∅ must occur in the power set of every set, including the empty set itself. The universal set or singleton sets are not guaranteed to be subsets of every possible set. Therefore, option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
