Question

Write the set of points from −2 to 6 but excluding 3 and 6 as a union of intervals:

Answer 1

The set of points from −2 to 6 excluding 3 and 6 is represented by the union of intervals (−2, 3) ∪ (3, 6).

Step-by-step explanation:

We need to express the set of points from −2 to 6 but excluding 3 and 6 as a union of intervals. The interval should start at −2 and end just before 3 because 3 is excluded. It should resume again right after 3 and continue up to but not including 6. Therefore, we can write this as a union of two intervals: (−2, 3) ∪ (3, 6). This indicates that the set includes all points from −2 up to but not including 3, and from just after 3 up to but not including 6.

Answer 2

[-2,6] - {3} - {6} = [-2,3) ∪ (3,6)

Step-by-step explanation:

Union Of Intervals

Let us assume two interval A = (a,b) and C = (c,d).

Their union is written as : A ∪ C = (a,b) ∪ (c,d)

Now, if interval is written in form [a,b] ⇒ a and b are INCLUDED in interval

Also, if interval is written in form (a,b) ⇒ a and b are NOT INCLUDED in interval

Here, the given interval is [-2,6]

excluding 3 and 6 from this will give:

[-2,3) ∪ (3,6)

The first set is [-2.3) where -2 is INCLUDED but 3 is NOT INCLUDED.

The second set is (3,6) where 3 and 6 both are NOT INCLUDED.

Hence, [-2,6] - {3} - {6} = [-2,3) ∪ (3,6)