Refer to the sets A, B, C, and D. Determine the union or...

Refer to the sets $A, B, C$, and $D$. Determine the union or intersection as indicated. Express the answer in interval notation, if possible. (see Example 2 )
$$A=\{x | x<-4\}, \quad B=\{x | x>2\}, \quad C=\{x | x \geq-7\}, \quad D=\{x | 0 \leq x<5\}$$
$$B \cap C$$

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Key Concepts

Inequalities

Inequalities are mathematical expressions that describe the relationship between two values when they are not equal. In the context of sets, inequalities help define continuous ranges of numbers. Understanding how to manipulate and combine inequalities is crucial for determining intersections or unions of sets based on their defined conditions.

Set Intersection

The intersection of two sets is a new set that contains all the elements that are common to both original sets. In set theory, this operation is typically denoted by the symbol ?. Understanding this concept is key to determining which elements satisfy the conditions of both sets simultaneously.

Interval Notation

Interval notation is a standardized method of representing subsets of the real numbers as intervals. It uses brackets [ ] to indicate that an endpoint is included (closed interval) and parentheses ( ) to denote that an endpoint is excluded (open interval). This notation simplifies the expression of continuous ranges of values defined by inequalities.

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