Question

Union and intersection of intervals - What is the union of the intervals [1, 3] and [2, 4]?

a) [1, 4]
b) [2, 3]
c) [1, 2] U [3, 4]
d) [1, 2, 3, 4]

Answer 1

The union of the intervals [1, 3] and [2, 4] is [1, 4], as it includes all numbers that are in either interval, forming a single continuous interval from 1 to 4.

Step-by-step explanation:

The question asks for the union of two intervals, [1, 3] and [2, 4]. The union of two intervals includes all the numbers that are in either interval. In this case, the union would include every number from 1 through 4, since the intervals overlap. Therefore, the correct answer is [1, 4].

To visualize this, imagine drawing both intervals on a number line. The interval [1, 3] spans from 1 to 3, including the end points. The interval [2, 4] spans from 2 to 4, also including the end points. The overlapping section would be from 2 to 3, but when taking the union, we combine all unique values covered by both intervals. This gives us a single, contiguous interval from the lowest point in either interval (1) to the highest point (4).