Identifying Connected Sets Quiz

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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 15 | Updated: Dec 1, 2025
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1) The interval (0,1) ∪ (1,2) is connected in ℝ.

Explanation

There is a gap at 1; the set splits into two separate intervals.

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About This Quiz
Identifying Connected Sets Quiz - Quiz

Think you can tell when a set is connected? This quiz helps you apply connectedness rules to real sets on the number line. You’ll examine unions of intervals, discrete sets, half-open intervals, and sets with gaps to decide whether they remain in one piece or split apart. You’ll also explore... see morehow intersections affect connectedness and why integers and separated unions are disconnected. By the end, you’ll confidently classify sets in ℝ as connected or disconnected based on their structure. see less

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2) A half-open interval [0,2) in ℝ is connected.

Explanation

Any interval—open, closed, or half-open—is connected.

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3) The union of two connected sets that do not intersect is always connected.

Explanation

If they do not touch or overlap, the union has a gap → disconnected.

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4) Every bounded interval in ℝ is connected.

Explanation

All intervals in ℝ are connected, regardless of being bounded or unbounded.

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5) The set of all integers ℤ in ℝ is connected.

Explanation

ℤ is a discrete set with gaps everywhere → disconnected.

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6) Any set consisting of a single point is connected.

Explanation

A one-point set cannot be split into two nonempty parts.

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

Explanation

[0,3] is a full interval; all others have gaps.

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8) Which of the following sets is disconnected in ℝ?

Explanation

There is a gap between 1 and 2.

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9) The set [0,1) ∪ [1,2] is:

Explanation

The sets meet at 1, forming interval [0,2].

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10) Which property must a connected set in ℝ satisfy?

Explanation

Connected subsets of ℝ are exactly intervals.

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11) Which of the following sets are connected?

Explanation

(−∞,0] and [−1,1] are intervals; the others have gaps.

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12) Which of the following sets in ℝ are disconnected?

Explanation

(0,1) ∪ (2,3) and {0,1,2} have gaps.

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13) Let A=[0,1], B=[2,3], C=[1,2]. Which unions are connected?

Explanation

A∪C and B∪C touch; all three form [0,3].

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14) Which of the following sets in ℝ are connected?

Explanation

All are intervals or singletons; [0,1]∪[2,3] has a gap.

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15) Which statements are true regarding connected sets in ℝ?

Explanation

Intervals are connected; discrete multi‑point sets are disconnected.

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The interval (0,1) ∪ (1,2) is connected in ℝ.
A half-open interval [0,2) in ℝ is connected.
The union of two connected sets that do not intersect is always...
Every bounded interval in ℝ is connected.
The set of all integers ℤ in ℝ is connected.
Any set consisting of a single point is connected.
Which of the following sets in ℝ is connected?
Which of the following sets is disconnected in ℝ?
The set [0,1) ∪ [1,2] is:
Which property must a connected set in ℝ satisfy?
Which of the following sets are connected?
Which of the following sets in ℝ are disconnected?
Let A=[0,1], B=[2,3], C=[1,2]. Which unions are connected?
Which of the following sets in ℝ are connected?
Which statements are true regarding connected sets in ℝ?
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