Question

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

Answer 1

Answer:

[-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)