Question

Take (In​ ) n∈{1,2,3,4} to be the finite sequence of intervals that is given by I 1​ =[−1,6),I 2​ =(−2,4),I 3 =[1,8], and 4​ =(0,3).

(a) Determine the union ⋃n∈{1,2,3,4}​ I n;

Answer 1

The union of the intervals I1=[−1,6), I2=(−2,4), I3=[1,8], and I4=(0,3) is the interval [−2,8], the comprehensive set that encompasses all individual intervals.

Step-by-step explanation:

To find the union ⋃n∈{1,2,3,4}​ In of the given intervals I1=[−1,6), I2=(−2,4), I3=[1,8], and I4=(0,3), we need to determine the comprehensive set of numbers that are included in any of the intervals. We do this by looking at the least and the greatest numbers included in the intervals and combining the overlapping sections:

• From I1 we have all numbers from −1 (inclusive) to 6 (exclusive).
• From I2 we exclude the endpoints, so numbers between −2 and 4.
• From I3 we have all numbers from 1 (inclusive) to 8 (inclusive).
• From I4 we have numbers from 0 (exclusive) to 3 (exclusive).

The union of these intervals will be [−2,8], which is the smallest interval that contains all other intervals.