If K₁ = {x : x ∈ ℤ, |x| = 0}, what type of set is K₁?
Answer and explanation
Correct answer: Singleton set
The absolute value |x| represents the distance of x from zero, so it can equal zero only when x = 0. Since 0 is an integer, it belongs to the stated domain. Hence K₁ = {0}. A set containing exactly one distinct element is called a singleton set. There are not two solutions, because |0| = 0 has only the single solution x = 0.
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What is the correct answer to this question?
Singleton set
Why is this the correct answer?
The absolute value |x| represents the distance of x from zero, so it can equal zero only when x = 0. Since 0 is an integer, it belongs to the stated domain. Hence K₁ = {0}. A set containing exactly one distinct element is called a singleton set. There are not two solutions, because |0| = 0 has only the single solution x = 0.
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.
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