How to write the union and intersection of two sets using interval notation?

Question

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}

 

my answers where (-infinity, 1] and no solution however both answers are incorrect, please help

Answer 1

As Michael explains, B can be written in interval notation as [1, ∞) and C can be written in interval notation as (-∞, 8).

 

 

The union of two sets is all values that are present in either set. Since C includes all values from -∞ to 8 (not including 8) and B includes all values from 1 to infinity, together they include every number. So their union is:

 

B∪C = (-∞, ∞)

 

 

The intersection of two set is all values that are present in both sets. Every number between 1 and 8 (including 1 but not 8) is present in both sets. So their intersection is:

 

B∩C = [1, 8)

Answer 2

Set B is all values of v equal to or greater than 1. 

 

B = [1, ∞)

 

The bracket indicates that 1 is included in the solution set.

 

 

Set C is all value of v less than 8.

 

C = (-∞, 8)

 

 

The interval that these sets have in common is

 

(1, 8)