Let N = {1, 2, 3, ...}. Choose the correct identification of A = {x ∈ N : 1 < x < 2}.
Answer and explanation
Correct answer: A = ∅
The notation 1 < x < 2 requires x to be strictly greater than 1 and strictly less than 2. Under the explicitly stated convention N = {1, 2, 3, ...}, there is no natural number satisfying both conditions. The numbers 1 and 2 are boundary values and are excluded by the strict inequalities. Therefore 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?
The notation 1 < x < 2 requires x to be strictly greater than 1 and strictly less than 2. Under the explicitly stated convention N = {1, 2, 3, ...}, there is no natural number satisfying both conditions. The numbers 1 and 2 are boundary values and are excluded by the strict inequalities. Therefore 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.
