Hello, I have been trying to do my math homework for a few hours now and can not figure out how to find the indicated intersection or union in interval notation.
Example: (-1,5)n[0,8)
Please help me!!
Draw two number lines, one under the other
(-1,5) extends from -1 to 5
underneath,
[0,8) extends from 0 to 8
The intersection is just where the intervals overlap: [0,5)
Thank You Steve. Now I understand the intersection. Could you please explain the union now.
Ecample: (-1,1)U[0,6]
Of course, I can help you with that!
To find the intersection of two sets in interval notation, you need to determine the values that are common to both sets. The symbol for intersection is "∩".
In your example, you have two sets: (-1, 5) and [0, 8).
First, let's represent these sets visually on a number line:
Set A: (-1, 5)
-------------------------
-1 5
Set B: [0, 8)
-------------------------
0 8
To find the intersection, analyze where both sets overlap.
From the number line, you can see that both sets overlap from 0 to 5, but exclude the endpoints -1 and 8.
Therefore, the intersection of (-1, 5) and [0, 8) is (0, 5).
Now, let's represent it in interval notation: (0, 5).
To find the union of two sets in interval notation, you need to determine all the values that belong in either set or both sets. The symbol for union is "∪".
Using the same example, (-1, 5) ∪ [0, 8):
From the number line representation, you can see that the union includes all values from -1 to 5, as well as 0 and 8.
Combining these intervals and removing duplicates, we have:
(-1, 8)
So, the union of (-1, 5) and [0, 8) is (-1, 8) in interval notation.
I hope this explanation helps you understand how to find the intersection and union of sets in interval notation for future use. Let me know if you have any further questions!