(-∞, -2)U(0,2)
The expression (-∞, -2) U (0, 2) represents the union of two intervals: the interval from negative infinity to negative 2, and the interval from 0 to 2
The expression (-∞, -2) U (0, 2) represents the union of two intervals: the interval from negative infinity to negative 2, and the interval from 0 to 2.
To understand this interval notation, let’s break it down.
The symbol “U” stands for union, which means that we combine the two separate intervals into one set.
The first interval (-∞, -2) represents all real numbers that are greater than negative infinity and less than negative 2. However, it does not include -2 itself. This is indicated by the use of parentheses around -∞ and -2.
The second interval (0, 2) represents all real numbers that are greater than 0 and less than 2. Similarly, it does not include 0 and 2 themselves.
Combining these two intervals gives us a set of numbers that are greater than negative infinity, less than negative 2, greater than 0, and less than 2. In other words, it includes all real numbers within the range from negative 2 to 0.
Graphically, you can represent this interval as an open interval on a number line. You would mark an open circle at -2 and another at 0, then shade the line between them, excluding the two marked points.
To summarize, the interval (-∞, -2) U (0, 2) represents all real numbers greater than negative infinity, less than negative 2, greater than 0, and less than 2.
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