Connected Sets Problem-Solving Quiz

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| Questions: 15 | Updated: Dec 1, 2025
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1) Let A=[0,1] and B=[1,2] in ℝ. Which of the following is true?

Explanation

They meet at 1, so [0,2] is a single interval → connected.

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About This Quiz
Connected Sets Problem-solving Quiz - Quiz

Ready to put your connectedness reasoning to the test? This quiz challenges you with real problem-solving scenarios involving unions of intervals, identifying connected components, and determining when adding or removing pieces affects connectedness. You'll work with sets that have gaps, shared endpoints, or overlapping intervals, and analyze how these features... see moreinfluence whether the union stays connected. By the end, you’ll be skilled at evaluating connectedness using logical reasoning and the structure of subsets in ℝ. see less

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

Explanation

[0,3] is an interval. All others have gaps.

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3) If S=[0,1] ∪ [1.5,2], which modification will make it connected?

Explanation

Adding [1,1.5] fills the gap and creates the full interval [0,2].

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4) Let A=(−1,0) ∪ (0,1). What is the connected component of 0?

Explanation

0 is not included in either interval, so it stands alone.

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

Explanation

(−∞,0) is an interval. All others have gaps.

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6) The union of connected sets A=[0,1], B=[2,3], C=[1,2] is:

Explanation

All three join to form [0,3], a single interval.

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7) Which of the following intervals is not connected in ℝ?

Explanation

(1,2) ∪ (2,3) has a gap at 2.

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8) Which of the following sets is connected?

Explanation

(−2,2) is an interval; the others split into separate pieces.

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

Explanation

(0,1) and [0,1] are intervals; {0} is a singleton.

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10) Identify the connected sets:

Explanation

Both are intervals; the others have gaps.

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11) For the sets A=[0,2], B=[2,4], C=[5,6], which unions are connected?

Explanation

A and B meet at 2 → connected.

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12) Which of the following sets are connected?

Explanation

A is the full interval (−1,1]; C is an interval; D is a singleton.

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13) Which sets are disconnected?

Explanation

Both have gaps; the others are intervals.

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14) If A=(−1,1), B=[1,2], C=[2,3], which combinations form a connected union?

Explanation

A touches B at 1; B touches C at 2; ABC forms (−1,3].

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15) Identify connected sets in ℝ:

Explanation

Both are intervals; A and C contain gaps.

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Let A=[0,1] and B=[1,2] in ℝ. Which of the following is true?
Which of the following sets in ℝ is connected?
If S=[0,1] ∪ [1.5,2], which modification will make it connected?
Let A=(−1,0) ∪ (0,1). What is the connected component of 0?
Which of the following sets is connected in ℝ?
The union of connected sets A=[0,1], B=[2,3], C=[1,2] is:
Which of the following intervals is not connected in ℝ?
Which of the following sets is connected?
Which of the following sets in ℝ are connected?
Identify the connected sets:
For the sets A=[0,2], B=[2,4], C=[5,6], which unions are connected?
Which of the following sets are connected?
Which sets are disconnected?
If A=(−1,1), B=[1,2], C=[2,3], which combinations form a connected...
Identify connected sets in ℝ:
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