Challenging Problems with Closed Sets

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7060 | Total Attempts: 9,520,935
| Questions: 15 | Updated: Oct 13, 2025
Please wait...
Question 1 / 15
0 %
0/100
Score 0/100
1) Which set is closed under addition?

Explanation

Even+Even=Even, but primes and naturals fail in some cases.

Submit
Please wait...
About This Quiz
Challenging Problems With Closed Sets - Quiz

Think you’ve mastered closure? This quiz brings tough problems requiring deeper insight. Take this quiz to push your closure understanding further.

2)
We’ll put your name on your report, certificate, and leaderboard.
2) Which set is closed under subtraction?

Explanation

Integers allow negative results, so closure holds.

Submit
3) The set of odd integers is closed under addition.

Explanation

Odd+Odd=Even.

Submit
4) Which set is closed under multiplication?

Explanation

Multiplication keeps all these sets intact.

Submit
5) Which set is not closed under division?

Explanation

Integers divided may not yield integers.

Submit
6) Which of the following is closed under absolute value?

Explanation

Absolute values stay in the same set.

Submit
7) Which is closed under exponentiation?

Explanation

Non-negative integers raised to powers remain non-negative integers.

Submit
8) The set of negative integers is closed under multiplication.

Explanation

Negative×Negative=Positive integer (still an integer).

Submit
9) Which set is closed under square roots?

Explanation

Complex numbers include all roots.

Submit
10) Which set is closed under complement operation?

Explanation

Complements are subsets of U.

Submit
11) Finite sets can be closed under some operations.

Explanation

Example: {0,1} closed under multiplication.

Submit
12) Which set is not closed under subtraction?

Explanation

Odd−Odd=Even.

Submit
13) Which set is closed under squaring?

Explanation

Squaring any value stays in the set.

Submit
14) Which is closed under union?

Explanation

Unions of subsets remain subsets.

Submit
15) Which set is not closed under multiplication?

Explanation

Multiplying two primes (2×3=6) does not yield a prime.

Submit
View My Results
Cancel
  • All
    All (15)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Which set is closed under addition?
Which set is closed under subtraction?
The set of odd integers is closed under addition.
Which set is closed under multiplication?
Which set is not closed under division?
Which of the following is closed under absolute value?
Which is closed under exponentiation?
The set of negative integers is closed under multiplication.
Which set is closed under square roots?
Which set is closed under complement operation?
Finite sets can be closed under some operations.
Which set is not closed under subtraction?
Which set is closed under squaring?
Which is closed under union?
Which set is not closed under multiplication?
Alert!

Back to Top Back to top
Advertisement