Identifying Disconnected Sets Quiz

Reviewed by Jede Crisle Cortes Davila
Jede Crisle Cortes Davila, Bachelor of Engineering |
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Jede Crisle D. is a mathematics subject matter expert specializing in Algebra, Geometry, and Calculus. She focuses on developing clear, solution-driven mathematical explanations and has strong experience with LaTeX-based math content. She holds a Bachelor’s degree in Electronics and Communications Engineering.
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| Attempts: 11 | Questions: 15 | Updated: Jan 27, 2026
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1) Which of the following sets in ℝ is disconnected?

Explanation

(1,2) and (3,4) are two separated intervals → gap → disconnected.

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About This Quiz
Identifying Disconnected Sets Quiz - Quiz

Think you can spot disconnected sets at a glance? This quiz challenges you to identify which subsets of ℝ and ℝ² split into separate parts. You’ll evaluate unions of intervals, sets with gaps, discrete sets, and separated geometric structures. You’ll also explore how removing points affects connectedness, and learn when... see moresets remain in one piece despite unusual shapes. By the end, you’ll confidently classify sets as connected or disconnected using their structural and topological properties.
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2)

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2) {0} ∪ [1,2] in ℝ is:

Explanation

There is a gap between {0} and [1,2] → disconnected.

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3) Which of the following sets in ℝ is connected?

Explanation

(0,3) is a single interval; others have gaps.

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4) Set X = {x ∈ ℝ : x² ≥1 or x² ≤0} is:

Explanation

X = (−∞,−1] ∪ {0} ∪ [1,∞) → multiple separated pieces.

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5) Which is a disconnected subset of ℝ?

Explanation

{1/n} is scattered → disconnected.

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6) A = {x <0 or x>1} is:

Explanation

A = (−∞,0) ∪ (1,∞).

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7) Which is disconnected in ℝ²?

Explanation

Two disjoint horizontal lines → disconnected.

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8) Identify all disconnected sets:

Explanation

{1,2} isolated; (1,2) ∪ (3,4) gap.

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9) Which ℝ sets are disconnected?

Explanation

Finite>1 points and separated intervals.

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10) Which statements about disconnected sets are correct?

Explanation

A true, C true; others false.

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11) Disconnected in ℝ²:

Explanation

Two separate pieces.

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12) Which sets are disconnected in ℝ?

Explanation

Isolated points and gap intervals.

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13) Which sets are disconnected?

Explanation

ℤ is discrete; union intervals gap.

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14) Disconnected in ℝ²:

Explanation

Two lines separate; rest connected.

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15) Examples of disconnected ℝ sets?

Explanation

A and B have gaps.

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Jede Crisle Cortes Davila |Bachelor of Engineering |
College Expert
Jede Crisle D. is a mathematics subject matter expert specializing in Algebra, Geometry, and Calculus. She focuses on developing clear, solution-driven mathematical explanations and has strong experience with LaTeX-based math content. She holds a Bachelor’s degree in Electronics and Communications Engineering.
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Which of the following sets in ℝ is disconnected?
{0} ∪ [1,2] in ℝ is:
Which of the following sets in ℝ is connected?
Set X = {x ∈ ℝ : x² ≥1 or x² ≤0} is:
Which is a disconnected subset of ℝ?
A = {x <0 or x>1} is:
Which is disconnected in ℝ²?
Identify all disconnected sets:
Which ℝ sets are disconnected?
Which statements about disconnected sets are correct?
Disconnected in ℝ²:
Which sets are disconnected in ℝ?
Which sets are disconnected?
Disconnected in ℝ²:
Examples of disconnected ℝ sets?
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