Which option is correct for the set A = {x ∈ ℤ : 0 < x < 1}?
Answer and explanation
Correct answer: A = ∅
The condition requires x to be an integer strictly greater than 0 and strictly less than 1. There is no integer between 0 and 1: 0 is excluded because the inequality is strict, and 1 is also excluded for the same reason. Hence no element satisfies the defining condition, so A has 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 condition requires x to be an integer strictly greater than 0 and strictly less than 1. There is no integer between 0 and 1: 0 is excluded because the inequality is strict, and 1 is also excluded for the same reason. Hence no element satisfies the defining condition, so A has 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.
