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F and H are sets of real numbers defined as follows. F={w|w<3} H={w | w≤9} Write FU H and FN H using interval notation. If the set is empty, write Ø. FUH = 0 FOH = 0 (0,0) [0,0] (0,0) [0,0) Ø ∞ X -8 Ś

F and H are sets of real numbers defined as follows. F={w|w<3} H={w | w≤9} Write FU H and FN H using interval notation. If the set is empty, write Ø. FUH = 0 FOH = 0 (0,0) [0,0] (0,0) [0,0) Ø ∞ X -8 Ś

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 78E
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### F and H are sets of real numbers defined as follows. \[ F = \{w \mid w < 3\} \] \[ H = \{w \mid w \leq 9\} \] Write \( F \cup H \) and \( F \cap H \) using **interval notation**. If the set is **empty**, write \(\emptyset\). #### Interval Notation In interval notation, ranges of numbers are denoted using parentheses \(( \)) for open intervals and brackets \([ ]\) for closed intervals. For example, the set of all real numbers less than 3 is written as \((-\infty, 3)\), and the set of all real numbers less than or equal to 9 is written as \((-\infty, 9]\). ### Solution #### For the Union (\( F \cup H \)): The union of two sets \( F \) and \( H \) includes all elements from both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the union \( F \cup H \) will be: \[ F \cup H = (-\infty, 9] \] #### For the Intersection (\( F \cap H \)): The intersection of two sets \( F \) and \( H \) includes only the elements that are common to both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the intersection \( F \cap H \) will be: \[ F \cap H = (-\infty, 3) \] #### Representation 1. \( F \cup H = (-\infty, 9] \) 2. \( F \cap H = (-\infty, 3) \) ### Diagram Explanation In the provided diagram, there is an input area to select the correct interval notation for the union and intersection of the sets \( F \) and \( H \). - Ensure to select: - For \( F \cup H \), choose the interval notation representing \((-\infty, 9]\). - For \( F \cap H \), choose the interval notation representing \((-\infty, 3)\). This
Transcribed Image Text:### F and H are sets of real numbers defined as follows. \[ F = \{w \mid w < 3\} \] \[ H = \{w \mid w \leq 9\} \] Write \( F \cup H \) and \( F \cap H \) using **interval notation**. If the set is **empty**, write \(\emptyset\). #### Interval Notation In interval notation, ranges of numbers are denoted using parentheses \(( \)) for open intervals and brackets \([ ]\) for closed intervals. For example, the set of all real numbers less than 3 is written as \((-\infty, 3)\), and the set of all real numbers less than or equal to 9 is written as \((-\infty, 9]\). ### Solution #### For the Union (\( F \cup H \)): The union of two sets \( F \) and \( H \) includes all elements from both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the union \( F \cup H \) will be: \[ F \cup H = (-\infty, 9] \] #### For the Intersection (\( F \cap H \)): The intersection of two sets \( F \) and \( H \) includes only the elements that are common to both sets. Hence, since \( F \) includes all real numbers less than 3 and \( H \) includes all real numbers less than or equal to 9, the intersection \( F \cap H \) will be: \[ F \cap H = (-\infty, 3) \] #### Representation 1. \( F \cup H = (-\infty, 9] \) 2. \( F \cap H = (-\infty, 3) \) ### Diagram Explanation In the provided diagram, there is an input area to select the correct interval notation for the union and intersection of the sets \( F \) and \( H \). - Ensure to select: - For \( F \cup H \), choose the interval notation representing \((-\infty, 9]\). - For \( F \cap H \), choose the interval notation representing \((-\infty, 3)\). This
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