(-8,-2)U(0,2)U(5,∞)
The expression (-8,-2) U (0,2) U (5, ∞) represents the union of three intervals on the number line
The expression (-8,-2) U (0,2) U (5, ∞) represents the union of three intervals on the number line. Let’s break down each interval.
1. The interval (-8, -2) represents all real numbers between -8 and -2, excluding -8 and -2 themselves. In interval notation, this can be written as (-8, -2).
2. The interval (0, 2) represents all real numbers between 0 and 2, excluding 0 and 2 themselves. In interval notation, this can be written as (0, 2).
3. The interval (5, ∞) represents all real numbers greater than 5. The symbol ∞ represents infinity, so this interval continues indefinitely to the right. In interval notation, this can be written as (5, ∞).
To find the union of these three intervals, we combine all the numbers from each interval together. This gives us the set of all numbers that belong to at least one of the intervals.
From the first interval, we have all numbers between -8 and -2, excluding -8 and -2. So, (-8, -2) includes -7, -6, -5, -4, -3, -2.
From the second interval, we have all numbers between 0 and 2, excluding 0 and 2. So, (0, 2) includes 1.
From the third interval, we have all numbers greater than 5, so (5, ∞) includes 6, 7, 8, 9, 10, and so on.
Combining all these numbers together, we have (-7, -6, -5, -4, -3, -2, 1, 6, 7, 8, 9, 10, …).
Please note that this union is represented in interval notation, which means we list the numbers in ascending order and separate them with commas.
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