Math / Algebra

Question $F$ and $H$ are sets of real numbers defined as follows $\begin{array}{l} F=\{z \mid z>3\} \\ H=\{z \mid z \leq 8\} \end{array}$
Write $F \cap H$ and $F \cup H$ using interval notation.

Studdy Solution

STEP 1

1. $F$ is the set of all real numbers $z$ such that $z > 3$ .
2. $H$ is the set of all real numbers $z$ such that $z \leq 8$ .
3. The notation $\cap$ represents the intersection of sets, which includes all elements common to both sets.
4. The notation $\cup$ represents the union of sets, which includes all elements that are in either set or both sets.
5. Interval notation will be used to express the sets.

STEP 2

1. Determine the intersection $F \cap H$ and express it in interval notation.
2. Determine the union $F \cup H$ and express it in interval notation.

STEP 3

Identify the intersection $F \cap H$ by determining the values of $z$ that satisfy both $z > 3$ and $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$

STEP 4

The intersection $F \cap H$ includes all $z$ such that $z > 3$ and $z \leq 8$ . This can be written in interval notation.
$F \cap H = (3, 8]$

STEP 5

Identify the union $F \cup H$ by determining the values of $z$ that satisfy either $z > 3$ or $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$

STEP 6

The union $F \cup H$ includes all $z$ such that $z > 3$ or $z \leq 8$ . This can be written in interval notation.
$F \cup H = (-\infty, \infty)$
Solution: $F \cap H = (3, 8]$ $F \cup H = (-\infty, \infty)$

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Question $F$ and $H$ are sets of real numbers defined as follows $\begin{array}{l} F=\{z \mid z>3\} \\ H=\{z \mid z \leq 8\} \end{array}$
Write $F \cap H$ and $F \cup H$ using interval notation.

Studdy Solution

STEP 1

STEP 2

1. Determine the intersection $F \cap H$ and express it in interval notation.
2. Determine the union $F \cup H$ and express it in interval notation.

STEP 3

Identify the intersection $F \cap H$ by determining the values of $z$ that satisfy both $z > 3$ and $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$

STEP 4

The intersection $F \cap H$ includes all $z$ such that $z > 3$ and $z \leq 8$ . This can be written in interval notation.
$F \cap H = (3, 8]$

STEP 5

Identify the union $F \cup H$ by determining the values of $z$ that satisfy either $z > 3$ or $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$

STEP 6

The union $F \cup H$ includes all $z$ such that $z > 3$ or $z \leq 8$ . This can be written in interval notation.
$F \cup H = (-\infty, \infty)$
Solution: $F \cap H = (3, 8]$ $F \cup H = (-\infty, \infty)$

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QuestionFFF and HHH are sets of real numbers defined as follows F={z∣z>3}H={z∣z≤8}\begin{array}{l} F=\{z \mid z>3\} \\ H=\{z \mid z \leq 8\} \end{array}F={z∣z>3}H={z∣z≤8}​Write F∩HF \cap HF∩H and F∪HF \cup HF∪H using interval notation.

Studdy Solution

STEP 1

STEP 2

1. Determine the intersection F∩HF \cap HF∩H and express it in interval notation.2. Determine the union F∪HF \cup HF∪H and express it in interval notation.

STEP 3

Identify the intersection F∩HF \cap HF∩H by determining the values of zzz that satisfy both z>3z > 3z>3 and z≤8z \leq 8z≤8.F={z∣z>3} F = \{ z \mid z > 3 \} F={z∣z>3} H={z∣z≤8} H = \{ z \mid z \leq 8 \} H={z∣z≤8}

STEP 4

The intersection F∩HF \cap HF∩H includes all zzz such that z>3z > 3z>3 and z≤8z \leq 8z≤8. This can be written in interval notation.F∩H=(3,8] F \cap H = (3, 8] F∩H=(3,8]

STEP 5

Identify the union F∪HF \cup HF∪H by determining the values of zzz that satisfy either z>3z > 3z>3 or z≤8z \leq 8z≤8.F={z∣z>3} F = \{ z \mid z > 3 \} F={z∣z>3} H={z∣z≤8} H = \{ z \mid z \leq 8 \} H={z∣z≤8}

STEP 6

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Question $F$ and $H$ are sets of real numbers defined as follows $\begin{array}{l} F=\{z \mid z>3\} \\ H=\{z \mid z \leq 8\} \end{array}$
Write $F \cap H$ and $F \cup H$ using interval notation.

1. Determine the intersection $F \cap H$ and express it in interval notation.
2. Determine the union $F \cup H$ and express it in interval notation.

Identify the intersection $F \cap H$ by determining the values of $z$ that satisfy both $z > 3$ and $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$

The intersection $F \cap H$ includes all $z$ such that $z > 3$ and $z \leq 8$ . This can be written in interval notation.
$F \cap H = (3, 8]$

Identify the union $F \cup H$ by determining the values of $z$ that satisfy either $z > 3$ or $z \leq 8$ .
$F = \{ z \mid z > 3 \}$ $H = \{ z \mid z \leq 8 \}$