QuestionMatch each interval with the correct set builder expression.
1. $[a,+\infty)$
2. $[a, b)$
3. $(-\infty, b)$
4. $(a, b)$
5. $(a, b]$
6. $(-\infty,+\infty)$
7. $[a, b]$
8. $(-\infty, b]$
9. $(a,+\infty)$
Options: a. $\{x \mid a<x<b\}$ b. $\{x \mid a<x \leq b\}$ c. $\{x \mid a<x\}$ d. $\{x \mid a \leq x\}$ e. $\{x \mid x \leq b\}$ f. $\{x \mid x \in \mathbb{R}\}$ g. $\{x \mid a \leq x \leq b\}$ h. $\{x \mid a \leq x<b\}$ i. $\{x \mid x<b\}$

Studdy Solution

STEP 1

Assumptions1. The intervals are given in the form of $-\vee(a, b)$ , $-\vee[a, b]$ , $-\vee(a, b]$ , $-\vee[a, b)$ , $-\vee(a,+\infty)$ , $-\vee[a,+\infty)$ , $-\vee(-\infty, b)$ , $-\vee(-\infty, b]$ , $-\vee(-\infty,+\infty)$ . The set builder expressions are given as $\{x \mid a<x<b\}$ , $\{x \mid a<x \leq b\}$ , $\{x \mid a<x\}$ , $\{x \mid a \leq x\}$ , $\{x \mid x \leq b\}$ , $\{x \mid x \in \mathbb{R}\}$ , $\{x \mid a \leq x \leq b\}$ , $\{x \mid a \leq x<b\}$ , $\{x \mid x<b\}$

STEP 2

Match the interval $-\vee(a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , but not including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a<x<b\}$ .

STEP 3

Match the interval $-\vee[a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a \leq x \leq b\}$ .

STEP 4

Match the interval $-\vee(a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $b$ but not $a$ . The corresponding set builder expression is $\{x \mid a<x \leq b\}$ .

STEP 5

Match the interval $-\vee[a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ but not $b$ . The corresponding set builder expression is $\{x \mid a \leq x<b\}$ .

STEP 6

Match the interval $-\vee(a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than $a$ but not including $a$ . The corresponding set builder expression is $\{x \mid a<x\}$ .

STEP 7

Match the interval $-\vee[a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than or equal to $a$ . The corresponding set builder expression is $\{x \mid a \leq x\}$ .

STEP 8

Match the interval $-\vee(-\infty, b)$ with the set builder expression. This interval represents all real numbers less than $b$ but not including $b$ . The corresponding set builder expression is $\{x \mid x<b\}$ .

STEP 9

Match the interval $-\vee(-\infty, b]$ with the set builder expression. This interval represents all real numbers less than or equal to $b$ . The corresponding set builder expression is $\{x \mid x \leq b\}$ .

STEP 10

Match the interval $-\vee(-\infty,+\infty)$ with the set builder expression. This interval represents all real numbers. The corresponding set builder expression is $\{x \mid x \in \mathbb{R}\}$ .
The matches are as follows $-\vee(a, b)$ matches with $\{x \mid a<x<b\}$ $-\vee[a, b]$ matches with $\{x \mid a \leq x \leq b\}$ $-\vee(a, b]$ matches with $\{x \mid a<x \leq b\}$ $-\vee[a, b)$ matches with $\{x \mid a \leq x<b\}$ $-\vee(a,+\infty)$ matches with $\{x \mid a<x\}$ $-\vee[a,+\infty)$ matches with $\{x \mid a \leq x\}$ $-\vee(-\infty, b)$ matches with $\{x \mid x<b\}$ $-\vee(-\infty, b]$ matches with $\{x \mid x \leq b\}$ $-\vee(-\infty,+\infty)$ matches with $\{x \mid x \in \mathbb{R}\}$

Was this helpful?

Studdy Solution

STEP 1

STEP 2

Match the interval $-\vee(a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , but not including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a<x<b\}$ .

STEP 3

Match the interval $-\vee[a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a \leq x \leq b\}$ .

STEP 4

Match the interval $-\vee(a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $b$ but not $a$ . The corresponding set builder expression is $\{x \mid a<x \leq b\}$ .

STEP 5

Match the interval $-\vee[a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ but not $b$ . The corresponding set builder expression is $\{x \mid a \leq x<b\}$ .

STEP 6

Match the interval $-\vee(a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than $a$ but not including $a$ . The corresponding set builder expression is $\{x \mid a<x\}$ .

STEP 7

Match the interval $-\vee[a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than or equal to $a$ . The corresponding set builder expression is $\{x \mid a \leq x\}$ .

STEP 8

Match the interval $-\vee(-\infty, b)$ with the set builder expression. This interval represents all real numbers less than $b$ but not including $b$ . The corresponding set builder expression is $\{x \mid x<b\}$ .

STEP 9

Match the interval $-\vee(-\infty, b]$ with the set builder expression. This interval represents all real numbers less than or equal to $b$ . The corresponding set builder expression is $\{x \mid x \leq b\}$ .

STEP 10

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

STEP 2

Match the interval −∨(a,b)-\vee(a, b)−∨(a,b) with the set builder expression. This interval represents all real numbers between aaa and bbb, but not including aaa and bbb. The corresponding set builder expression is {x∣a<x<b}\{x \mid a<x<b\}{x∣a<x<b}.

STEP 3

Match the interval −∨[a,b]-\vee[a, b]−∨[a,b] with the set builder expression. This interval represents all real numbers between aaa and bbb, including aaa and bbb. The corresponding set builder expression is {x∣a≤x≤b}\{x \mid a \leq x \leq b\}{x∣a≤x≤b}.

STEP 4

Match the interval −∨(a,b]-\vee(a, b]−∨(a,b] with the set builder expression. This interval represents all real numbers between aaa and bbb, including bbb but not aaa. The corresponding set builder expression is {x∣a<x≤b}\{x \mid a<x \leq b\}{x∣a<x≤b}.

STEP 5

Match the interval −∨[a,b)-\vee[a, b)−∨[a,b) with the set builder expression. This interval represents all real numbers between aaa and bbb, including aaa but not bbb. The corresponding set builder expression is {x∣a≤x<b}\{x \mid a \leq x<b\}{x∣a≤x<b}.

STEP 6

Match the interval −∨(a,+∞)-\vee(a,+\infty)−∨(a,+∞) with the set builder expression. This interval represents all real numbers greater than aaa but not including aaa. The corresponding set builder expression is {x∣a<x}\{x \mid a<x\}{x∣a<x}.

STEP 7

Match the interval −∨[a,+∞)-\vee[a,+\infty)−∨[a,+∞) with the set builder expression. This interval represents all real numbers greater than or equal to aaa. The corresponding set builder expression is {x∣a≤x}\{x \mid a \leq x\}{x∣a≤x}.

STEP 8

Match the interval −∨(−∞,b)-\vee(-\infty, b)−∨(−∞,b) with the set builder expression. This interval represents all real numbers less than bbb but not including bbb. The corresponding set builder expression is {x∣x<b}\{x \mid x<b\}{x∣x<b}.

STEP 9

Match the interval −∨(−∞,b]-\vee(-\infty, b]−∨(−∞,b] with the set builder expression. This interval represents all real numbers less than or equal to bbb. The corresponding set builder expression is {x∣x≤b}\{x \mid x \leq b\}{x∣x≤b}.

STEP 10

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Match the interval $-\vee(a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , but not including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a<x<b\}$ .

Match the interval $-\vee[a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ and $b$ . The corresponding set builder expression is $\{x \mid a \leq x \leq b\}$ .

Match the interval $-\vee(a, b]$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $b$ but not $a$ . The corresponding set builder expression is $\{x \mid a<x \leq b\}$ .

Match the interval $-\vee[a, b)$ with the set builder expression. This interval represents all real numbers between $a$ and $b$ , including $a$ but not $b$ . The corresponding set builder expression is $\{x \mid a \leq x<b\}$ .

Match the interval $-\vee(a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than $a$ but not including $a$ . The corresponding set builder expression is $\{x \mid a<x\}$ .

Match the interval $-\vee[a,+\infty)$ with the set builder expression. This interval represents all real numbers greater than or equal to $a$ . The corresponding set builder expression is $\{x \mid a \leq x\}$ .

Match the interval $-\vee(-\infty, b)$ with the set builder expression. This interval represents all real numbers less than $b$ but not including $b$ . The corresponding set builder expression is $\{x \mid x<b\}$ .

Match the interval $-\vee(-\infty, b]$ with the set builder expression. This interval represents all real numbers less than or equal to $b$ . The corresponding set builder expression is $\{x \mid x \leq b\}$ .