Closed Sets Quiz (Advanced) � Analyze Closure and Logical Structure (MP.2, MP.7)

1) Closure under one operation implies closure under all?

Yes

No

Sometimes

Only for integers

Closure is operation-specific.

Explanation

Closure is operation-specific.

2) Which set is closed under intersection?

Power set of U

Integers

Rationals

Naturals

Intersection of subsets → subset.

Explanation

Intersection of subsets → subset.

3) Which set is closed under union?

Power set of U

Primes

Evens

Irrationals

Any union of subsets stays in power set.

Explanation

Any union of subsets stays in power set.

4) Which set is not closed under logarithms?

Positive reals

Non-positive numbers

Complex numbers

Naturals

log(−1) undefined in reals.

Explanation

log(−1) undefined in reals.

5) Complex numbers are closed under:

Addition

Subtraction

Multiplication

All of the above

Except division by 0, all operations work.

Explanation

Except division by 0, all operations work.

6) Odd integers under subtraction:

Closed

Not closed

Sometimes closed

Closed only under addition

3−5=−2 even.

Explanation

3−5=−2 even.

7) Perfect cubes are closed under:

Addition

Multiplication

Division

None

Cube×Cube=Cube.

Explanation

Cube×Cube=Cube.

8) Non-negative integers are not closed under:

Addition

Multiplication

Subtraction

None

2−5=−3 not non-negative.

Explanation

2−5=−3 not non-negative.

9) Which is not closed under division?

Integers

Rationals

Reals

Complex

Same reason: 1 ÷ 2 not integer.

Explanation

Same reason: 1 ÷ 2 not integer.

10) Closure under complement means:

Set repeats

Complement is in the same universal structure

Set is finite

All subsets equal

Complements belong to U.

Explanation

Complements belong to U.

11) Which set is closed under squaring?

Integers

Rationals

Reals

All

Square always remains valid.

Explanation

Square always remains valid.

12) Which set is not closed under square roots?

Reals

Non-negative reals

Complex numbers

Power set

√(−1) not real.

Explanation

√(−1) not real.

13) Empty set is closed under union.

True

False

∅ ∪ ∅ = ∅.

Explanation

∅ ∪ ∅ = ∅.

14) Whole numbers are closed under multiplication.

True

False

Multiplying whole numbers gives whole.

Explanation

Multiplying whole numbers gives whole.

15) Integers are closed under absolute value.

True

False

Abs of an integer is still integer.

Explanation

Abs of an integer is still integer.

Reasoning About Closure in Mathematics

1) Closure under one operation implies closure under all?

2)

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

2) Which set is closed under intersection?

3) Which set is closed under union?

4) Which set is not closed under logarithms?

5) Complex numbers are closed under:

6) Odd integers under subtraction:

7) Perfect cubes are closed under:

8) Non-negative integers are not closed under:

9) Which is not closed under division?

10) Closure under complement means:

11) Which set is closed under squaring?

12) Which set is not closed under square roots?

13) Empty set is closed under union.

14) Whole numbers are closed under multiplication.

15) Integers are closed under absolute value.