If A = {x : x is a natural number and x = x + 1}, what kind of set is A?
Answer and explanation
Correct answer: Empty set
The equation x = x + 1 cannot be true for any number. Subtracting x from both sides gives 0 = 1, which is a contradiction. Therefore, no natural number satisfies the defining condition of A. A set with no member is called the empty set, so A = ∅. It is finite as well, but the requested type is empty set.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
The equation x = x + 1 cannot be true for any number. Subtracting x from both sides gives 0 = 1, which is a contradiction. Therefore, no natural number satisfies the defining condition of A. A set with no member is called the empty set, so A = ∅. It is finite as well, but the requested type is empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
