If U₁ = {x : x ∈ ℕ, x leaves remainder 6 when divided by 6}, what is U₁?
Answer and explanation
Correct answer: Empty set
By the division algorithm, when a number is divided by a positive divisor 6, the remainder must be one of 0, 1, 2, 3, 4, or 5. A remainder must always be strictly less than the divisor. Therefore remainder 6 is impossible for every natural number. No x satisfies the defining condition, so U₁ has no elements and is the empty set, denoted by ∅.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
By the division algorithm, when a number is divided by a positive divisor 6, the remainder must be one of 0, 1, 2, 3, 4, or 5. A remainder must always be strictly less than the divisor. Therefore remainder 6 is impossible for every natural number. No x satisfies the defining condition, so U₁ has no elements and is the empty set, denoted by ∅.
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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