Reasoning About Closure in Mathematics

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| Questions: 15 | Updated: Oct 13, 2025
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1) Closure under one operation implies closure under all?

Explanation

Closure is operation-specific.

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About This Quiz
Reasoning About Closure In Mathematics - Quiz

Closure is about explanation as much as calculation. In this quiz, you’ll reason why certain sets are (or aren’t) closed. Try this quiz to strengthen mathematical logic.

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2) Which set is closed under intersection?

Explanation

Intersection of subsets → subset.

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3) Which set is closed under union?

Explanation

Any union of subsets stays in power set.

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4) Which set is not closed under logarithms?

Explanation

log(−1) undefined in reals.

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5) Complex numbers are closed under:

Explanation

Except division by 0, all operations work.

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6) Odd integers under subtraction:

Explanation

3−5=−2 even.

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7) Perfect cubes are closed under:

Explanation

Cube×Cube=Cube.

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8) Non-negative integers are not closed under:

Explanation

2−5=−3 not non-negative.

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9) Which is not closed under division?

Explanation

Same reason: 1 ÷ 2 not integer.

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10) Closure under complement means:

Explanation

Complements belong to U.

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11) Which set is closed under squaring?

Explanation

Square always remains valid.

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12) Which set is not closed under square roots?

Explanation

√(−1) not real.

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13) Empty set is closed under union.

Explanation

∅ ∪ ∅ = ∅.

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14) Whole numbers are closed under multiplication.

Explanation

Multiplying whole numbers gives whole.

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15) Integers are closed under absolute value.

Explanation

Abs of an integer is still integer.

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Closure under one operation implies closure under all?
Which set is closed under intersection?
Which set is closed under union?
Which set is not closed under logarithms?
Complex numbers are closed under:
Odd integers under subtraction:
Perfect cubes are closed under:
Non-negative integers are not closed under:
Which is not closed under division?
Closure under complement means:
Which set is closed under squaring?
Which set is not closed under square roots?
Empty set is closed under union.
Whole numbers are closed under multiplication.
Integers are closed under absolute value.
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