If A = {x ∈ N : x is less than 100 and x is greater than 100}, which option is correct?
Answer and explanation
Correct answer: A = ∅
The conditions x < 100 and x > 100 must hold simultaneously. No number, whether natural, integer, or real, can be both less than 100 and greater than 100 at the same time. Thus, there is no natural number satisfying the definition of A. Consequently, A contains no elements and is the empty set, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The conditions x < 100 and x > 100 must hold simultaneously. No number, whether natural, integer, or real, can be both less than 100 and greater than 100 at the same time. Thus, there is no natural number satisfying the definition of A. Consequently, A contains no elements and is the empty set, so option A is correct.
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.
