If T = {x : x ∈ ℕ, x > 1 and x has exactly one positive factor}, what is T?
Answer and explanation
Correct answer: T = ∅
The only natural number with exactly one positive factor is 1, because its only positive divisor is 1. However, the definition of T also requires x > 1, which excludes 1. Every natural number greater than 1 has at least two positive factors, namely 1 and the number itself. Therefore, no value satisfies both conditions, so T is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
T = ∅
Why is this the correct answer?
The only natural number with exactly one positive factor is 1, because its only positive divisor is 1. However, the definition of T also requires x > 1, which excludes 1. Every natural number greater than 1 has at least two positive factors, namely 1 and the number itself. Therefore, no value satisfies both conditions, so T 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.
