Testing Closure with Operations

  • 11th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
Review Board Member
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.
 , MBA
By Thames
T
Thames
Community Contributor
Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 15 | Updated: Jan 21, 2026
Please wait...
Question 1 / 16
🏆 Rank #-- ▾
Score 0/100

1) Odd integers are closed under:

Explanation

Odd×Odd=Odd.

Submit
Please wait...
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.

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) Perfect squares are closed under:

Explanation

Square×Square=Square.

Submit

3) Which set is closed under complement?

Explanation

Complements always subsets of U.

Submit

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

Explanation

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

Submit

5) Which is not closed under division?

Explanation

1 ÷ 2 not integer.

Submit

6) Whole numbers are closed under:

Explanation

Addition keeps them whole.

Submit

7) Which set is closed under absolute value?

Explanation

Abs always stays in set.

Submit

8) Which set is closed under exponentiation?

Explanation

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

Submit

9) Which set is not closed under square roots?

Explanation

√2 not integer.

Submit

10) Which set is closed under subtraction?

Explanation

Difference of evens → even.

Submit

11) Which set is not closed under addition?

Explanation

Prime+Prime not always prime.

Submit

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

Explanation

Negation keeps set intact.

Submit

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

Explanation

Division by 0 breaks closure.

Submit

14) Irrationals are closed under multiplication.

Explanation

√2 × √2 = 2, not irrational.

Submit

15) Complex numbers are closed under subtraction.

Explanation

Subtracting complex numbers gives complex.
Submit
×
Saved
Thank you for your feedback!
View My Results
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.
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
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.
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!