Still having trouble with figuing the union and intersection of these two sets below

Question

How to write the union and intersection of two sets using interval notation?
I'm trying to figure out the union and intersection of these two sets (below) using  interval notation for these problems
 
B={v|v>=1}
C={v|v<8}

Answer 1

Union:

(-∞, ∞)

Intersection:

[1, 8)

 

I'll try my best to "draw" an explanation:

 

 <-------------------------------------O       think of this upper ray as a semi-transparent cover for the "walkway"

      *------------------------------------------------------------>     this lower ray is also semi-transparent

<---*---------------------------------O-------------------------------->   think of this line as the "walkway"

      1                                          8

 

So what we have is an imaginary covered walkway with 2 roofs.  Both roofs are tinted, providing shade for the sidewalk.

No roof = sunny, bright sidewalk

1 roof  = dimly lit sidewalk

2 roofs = too dark to see

 

Stay with me...

Union = shaded sidewalk (whether dim or dark)         Intersection = dark sidewalk only

 

Union:  

    Together the upper and lower rays provide some level of shading for the entire sidewalk (-∞, ∞)

 

Intersection:

    All light between 1 and 8 is blocked out since that part of the sidewalk has 2 roofs that together let NO light through.

    HOWEVER, the upper roof doesn't cover 8 and the undimmed light that makes it through the upper roof at 8 can

    only be dimmed by the lower roof.  No light makes it through the 2 roofs that both cover 1

    on the sidewalk.

 

   The dark part of the sidewalk then is from [1,8) , 8 not included because it is not totally dark there.

 

I know, crazy, huh?  I don't just make this kind of stuff up for my students, I do it for myself as well.

Answer 2

Union ∪ means that we have to include two sets of solutions separately.  Intersection means that we have solutions that the two sets have in common.

 

Set B = [1, ∞)

Set C = (-∞, 8)

 

 

Union:

 

(-∞, 1)∪(1, ∞)

 

 

Intersection:

 

(1, 8)