Identifying Closure in Different Sets

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 15 | Updated: Jan 21, 2026
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1) Integers are not closed under:

Explanation

1 ÷ 2 is not an integer.

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About This Quiz
Identifying Closure In Different Sets - Quiz

Explore whether operations keep you “inside” a set. In this quiz, you’ll test closure across integers, rationals, and reals. Try this quiz to learn the basics of closure.

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2) Which operation keeps natural numbers closed?

Explanation

Naturals remain closed under addition.

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3) If A={multiples of 5}, then A is closed under:

Explanation

Multiples of 5 stay multiples of 5.

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4) Prime numbers are closed under addition?

Explanation

3+5=8 not prime.

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5) Universal set is always closed under:

Explanation

Union/intersection never leave U.

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6) Whole numbers are closed under addition.

Explanation

Addition keeps them whole.

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7) Integers are closed under multiplication.

Explanation

Multiplying integers gives integers.

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8) A set is closed under an operation if:

Explanation

Closure means all results remain in the set.

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9) Even integers are closed under:

Explanation

Sum/product of evens is even.

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10) Rational numbers are closed under:

Explanation

Rationals stay rationals under these.

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11) Which set is closed under square roots?

Explanation

Only non-negative reals guarantee closure.

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12) Irrationals are not closed under:

Explanation

√2 + (−√2) = 0, not irrational.

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13) Which set is closed under subtraction?

Explanation

Subtracting two integers gives an integer.

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14) {0,1} under multiplication is:

Explanation

0×0=0, 1×1=1, 0×1=0.

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15) Naturals are closed under subtraction.

Explanation

3-5=-2 not natural.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Integers are not closed under:
Which operation keeps natural numbers closed?
If A={multiples of 5}, then A is closed under:
Prime numbers are closed under addition?
Universal set is always closed under:
Whole numbers are closed under addition.
Integers are closed under multiplication.
A set is closed under an operation if:
Even integers are closed under:
Rational numbers are closed under:
Which set is closed under square roots?
Irrationals are not closed under:
Which set is closed under subtraction?
{0,1} under multiplication is:
Naturals are closed under subtraction.
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