Testing Closure with Operations

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| By Thames
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Thames
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Quizzes Created: 7060 | Total Attempts: 9,520,935
| Questions: 15 | Updated: Oct 13, 2025
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1) Odd integers are closed under:

Explanation

Odd×Odd=Odd.

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About This Quiz
Testing Closure With Operations - Quiz

Addition, multiplication, and beyond — do sets stay closed? In this quiz, you’ll test closure through different operations. Take this quiz to see how sets behave under rules.

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2) Perfect squares are closed under:

Explanation

Square×Square=Square.

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3) Which set is closed under complement?

Explanation

Complements always subsets of U.

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4) {x ∈ Z | x multiple of 7} is closed under:

Explanation

Sum/difference of multiples of 7 → multiple of 7.

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5) Which is not closed under division?

Explanation

1 ÷ 2 not integer.

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6) Whole numbers are closed under:

Explanation

Addition keeps them whole.

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7) Which set is closed under absolute value?

Explanation

Abs always stays in set.

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8) Which set is closed under exponentiation?

Explanation

Any non-negative integer power is non-negative integer.

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9) Which set is not closed under square roots?

Explanation

√2 not integer.

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10) Which set is closed under subtraction?

Explanation

Difference of evens → even.

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11) Which set is not closed under addition?

Explanation

Prime+Prime not always prime.

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12) Which set is closed under negation (−x)?

Explanation

Negation keeps set intact.

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13) Rationals are closed under division (except by 0).

Explanation

Division by 0 breaks closure.

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14) Irrationals are closed under multiplication.

Explanation

√2 × √2 = 2, not irrational.

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15) Complex numbers are closed under subtraction.

Explanation

Subtracting complex numbers gives complex.
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Odd integers are closed under:
Perfect squares are closed under:
Which set is closed under complement?
{x ∈ Z | x multiple of 7} is closed under:
Which is not closed under division?
Whole numbers are closed under:
Which set is closed under absolute value?
Which set is closed under exponentiation?
Which set is not closed under square roots?
Which set is closed under subtraction?
Which set is not closed under addition?
Which set is closed under negation (−x)?
Rationals are closed under division (except by 0).
Irrationals are closed under multiplication.
Complex numbers are closed under subtraction.
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