If A is the set of natural numbers x such that x is a three-digit number and x < 100, what is A?
Answer and explanation
Correct answer: A = ∅
A three-digit natural number must be at least 100; the three-digit numbers begin with 100 and continue through 999. The additional condition x < 100 contradicts the requirement that x have three digits. Hence there is no natural number satisfying both conditions, so A contains no elements and is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
A three-digit natural number must be at least 100; the three-digit numbers begin with 100 and continue through 999. The additional condition x < 100 contradicts the requirement that x have three digits. Hence there is no natural number satisfying both conditions, so A contains no elements and is the empty set, written as ∅.
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.
