Choose the correct option for A = {x ∈ ℤ : x is positive and x is negative}.
Answer and explanation
Correct answer: A = ∅
The condition requires an integer to be positive and negative at the same time. No integer has both properties. Positive integers are greater than zero, while negative integers are less than zero; these two classes do not overlap. Zero does not provide an exception because it is neither positive nor negative. Hence no integer satisfies the defining condition, and A is the empty set ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The condition requires an integer to be positive and negative at the same time. No integer has both properties. Positive integers are greater than zero, while negative integers are less than zero; these two classes do not overlap. Zero does not provide an exception because it is neither positive nor negative. Hence no integer satisfies the defining condition, and A is the empty set ∅.
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.
