If A = {∅, {∅}}, which of the following is not a subset of A?
Answer and explanation
Correct answer: {∅, {{∅}}}
The set A has exactly two elements: ∅ and {∅}. Its subsets are ∅, {∅}, {{∅}}, and {∅, {∅}}. Option D is {∅, {{∅}}}; it contains the element {{∅}}, but {{∅}} is not an element of A. A contains {∅}, not {{∅}}. Therefore every element of option D is not in A, so option D is not a subset. Careful counting of nested braces is essential in this question.
Frequently asked questions
What is the correct answer to this question?
{∅, {{∅}}}
Why is this the correct answer?
The set A has exactly two elements: ∅ and {∅}. Its subsets are ∅, {∅}, {{∅}}, and {∅, {∅}}. Option D is {∅, {{∅}}}; it contains the element {{∅}}, but {{∅}} is not an element of A. A contains {∅}, not {{∅}}. Therefore every element of option D is not in A, so option D is not a subset. Careful counting of nested braces is essential in this question.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
