Closed Sets Quiz (Mixed Concepts) � Review Closure under Mathematical Operations (MP.2, MP.7)

1) Which set is closed under addition?

Evens

Primes

Naturals

None

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

Explanation

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

2) Which set is closed under subtraction?

Integers

Whole numbers

Naturals

Non-negative integers

Integers allow negative results, so closure holds.

Explanation

Integers allow negative results, so closure holds.

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

True

False

Odd+Odd=Even.

Explanation

Odd+Odd=Even.

4) Which set is closed under multiplication?

Integers

Reals

Rationals

All of the above

Multiplication keeps all these sets intact.

Explanation

Multiplication keeps all these sets intact.

5) Which set is not closed under division?

Rationals

Reals

Integers

Complex numbers

Integers divided may not yield integers.

Explanation

Integers divided may not yield integers.

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

Integers

Rationals

Reals

All

Absolute values stay in the same set.

Explanation

Absolute values stay in the same set.

7) Which is closed under exponentiation?

Non-negative integers

Negative integers

Primes

None

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

Explanation

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

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

True

False

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

Explanation

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

9) Which set is closed under square roots?

Complex numbers

Reals

Integers

Naturals

Complex numbers include all roots.

Explanation

Complex numbers include all roots.

10) Which set is closed under complement operation?

Power set of U

Integers

Naturals

Primes

Complements are subsets of U.

Explanation

Complements are subsets of U.

11) Finite sets can be closed under some operations.

True

False

Example: {0,1} closed under multiplication.

Explanation

Example: {0,1} closed under multiplication.

12) Which set is not closed under subtraction?

Even integers

Odd integers

Integers

Rationals

Odd−Odd=Even.

Explanation

Odd−Odd=Even.

13) Which set is closed under squaring?

Integers

Rationals

Reals

All

Squaring any value stays in the set.

Explanation

Squaring any value stays in the set.

14) Which is closed under union?

Power set of U

Integers

Reals

Irrationals

Unions of subsets remain subsets.

Explanation

Unions of subsets remain subsets.

15) Which set is not closed under multiplication?

Even integers

Odd integers

Primes

Rationals

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

Explanation

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

Challenging Problems with Closed Sets

1) Which set is closed under addition?

2)

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

2) Which set is closed under subtraction?

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

4) Which set is closed under multiplication?

5) Which set is not closed under division?

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

7) Which is closed under exponentiation?

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

9) Which set is closed under square roots?

10) Which set is closed under complement operation?

11) Finite sets can be closed under some operations.

12) Which set is not closed under subtraction?

13) Which set is closed under squaring?

14) Which is closed under union?

15) Which set is not closed under multiplication?