Boundedness: Real-World Applications Quiz

1) A GPS system models positions of delivery vehicles as points in ℝ² within a 10 km × 10 km city grid. Which statement is true?

A. The set of vehicle positions is unbounded

B. The set of vehicle positions is bounded

C. The set is bounded only along one axis

D. The set is unbounded in time

All positions lie within a finite square region, so the set is bounded.

Explanation

All positions lie within a finite square region, so the set is bounded.

2) In an online rating system, user ratings lie in the interval [0,5]. Which statements are correct?

A. The set of all ratings is bounded

B. The set is bounded above

C. The set is bounded below

D. The set is unbounded

Ratings are always between 0 and 5, so they are bounded above and below.

Explanation

Ratings are always between 0 and 5, so they are bounded above and below.

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3) A drone maps an area and records altitude values h(x,y) with 0 ≤ h(x,y) ≤ 200 meters. Which is true?

A. The altitude set is bounded

B. The altitude set is unbounded

C. The altitude set is bounded below only

D. The altitude set is bounded above only

The altitudes lie in a finite interval [0,200].

Explanation

The altitudes lie in a finite interval [0,200].

4) Temperature sensors record values Ti with −5 ≤ Ti ≤ 40. Which are correct?

A. The set of recorded temperatures is bounded

B. The maximum temperature difference is ≤ 45

C. A subset of temperatures above 0 is unbounded

D. A subset of temperatures between −5 and 10 is bounded

All temperatures lie within a finite range; subsets stay bounded unless the range is infinite.

Explanation

All temperatures lie within a finite range; subsets stay bounded unless the range is infinite.

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5) A company monitors truck positions along a 100 km highway. What is the set of positions in ℝ?

A. Bounded between 0 and 100

B. Unbounded because trucks move

C. Bounded only in the positive direction

D. Empty

All positions lie in the finite interval [0,100].

Explanation

All positions lie in the finite interval [0,100].

6) A smartphone tracks a user's location in a 500 m m 500 m park. Which statements are correct?

A. Bounded in x-direction

B. Bounded in y-direction

C. Bounded in both directions

D. Unbounded because the user can walk anywhere

The park dimensions impose finite bounds on both axes.

Explanation

The park dimensions impose finite bounds on both axes.

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7) Delivery times in hours lie between 0.5 and 72. Which is true?

A. Bounded

B. Unbounded

C. Bounded below only

D. Bounded above only

The set lies in the finite interval [0.5,72].

Explanation

The set lies in the finite interval [0.5,72].

8) Robots move on a warehouse floor of size 10 m × 20 m. The set of robot positions is:

A. Bounded

B. Contains all real numbers

C. Bounded in x-axis

D. Bounded in y-axis

All positions lie in a finite rectangle, so the entire set is bounded.

Explanation

All positions lie in a finite rectangle, so the entire set is bounded.

9) ATM withdrawals range between $20 and $1000. The set of transaction amounts is:

A. Unbounded

B. Bounded

C. Bounded below only

D. Bounded above only

All amounts fall in the finite interval [20,1000].

Explanation

All amounts fall in the finite interval [20,1000].

10) Heart rates (bpm) satisfy 50 ≤ bpm ≤ 180. Which statements are correct?

A. The set of heart rates is bounded

B. The subset above 100 bpm is bounded

C. The subset below 50 bpm is bounded

D. The maximum difference is ≤ 130

All values lie in a finite interval; subsets remain bounded unless they extend infinitely.

Explanation

All values lie in a finite interval; subsets remain bounded unless they extend infinitely.

11) A delivery drone operates only inside a circle of radius 2 km. The set of all positions is:

A. Unbounded

B. Bounded

C. Empty

D. Bounded only in one dimension

A disk of radius 2 is a bounded region in ℝ².

Explanation

A disk of radius 2 is a bounded region in ℝ².

12) A smart thermostat measures temperatures between 18°C and 28°C.

A. The set of all temperatures is bounded

B. Any subset of temperatures is bounded

C. The set is bounded below only

D. The set is bounded above only

Temperatures lie within a finite interval; all subsets stay within that range.

Explanation

Temperatures lie within a finite interval; all subsets stay within that range.

13) Pollution index values lie in [0,500]. If new sensors measure only in [100,300], the original set is:

A. Bounded

B. Unbounded

C. Bounded only in the upper limit

D. Empty

The full set still lies within [0,500], which is bounded.

Explanation

The full set still lies within [0,500], which is bounded.

14) A ride-sharing app records trip distances in kilometers: 0.5 ≤ d ≤ 50. Which statements are correct?

A. The set of trip distances is bounded

B. The maximum distance difference is ≤ 49.5

C. A subset of trips longer than 30 km is bounded

D. The set is unbounded because some trips may be longer than 50 km

Distances lie in a finite closed interval; all subsets within this interval remain bounded.

Explanation

Distances lie in a finite closed interval; all subsets within this interval remain bounded.

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15) A company models office locations in a rectangle of width 10 km and height 5 km. Which is true?

A. The set of office locations is bounded

B. The set is unbounded

C. The set is bounded only in one direction

D. The set is empty

All positions lie in a finite rectangle, so the set is bounded.

Explanation

All positions lie in a finite rectangle, so the set is bounded.