If Z₁ = {x : x ∈ ℕ, x is a two-digit number, and x > 99}, what is Z₁?
Answer and explanation
Correct answer: Z₁ = ∅
A two-digit natural number ranges from 10 through 99, inclusive. The condition x > 99 asks for a two-digit number strictly greater than the largest possible two-digit number, 99. No such natural number exists. Consequently, the defining conditions cannot be satisfied simultaneously, and Z₁ contains no elements. Therefore Z₁ is the empty set, written as ∅; it is not the set containing 99 because the inequality is strict.
Frequently asked questions
What is the correct answer to this question?
Z₁ = ∅
Why is this the correct answer?
A two-digit natural number ranges from 10 through 99, inclusive. The condition x > 99 asks for a two-digit number strictly greater than the largest possible two-digit number, 99. No such natural number exists. Consequently, the defining conditions cannot be satisfied simultaneously, and Z₁ contains no elements. Therefore Z₁ is the empty set, written as ∅; it is not the set containing 99 because the inequality is strict.
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.
