Math / Discrete

QuestionHayden Boudreaux
This test: 100 point(s) possible This question: 3 point(s) Submit tes TEST \#2 Question 2 of 28 possible
If $A=\{x \mid x$ is an odd integer $\}$ and $B=\{x \mid x$ is an even integer greater than 0 $\}$ , list the elements of the set $A \cup B$ .
Choose the correct answer. A. $\{\ldots,-3,-1,1,3, \ldots\}$ B. $\{\ldots,-3,-1,1,2,3, \ldots\}$

Studdy Solution

STEP 1

1. Set $A$ consists of all odd integers.
2. Set $B$ consists of all even integers greater than 0.
3. The union of sets $A$ and $B$ includes all elements that are either in $A$ or in $B$ .

STEP 2

1. Define the set $A$ .
2. Define the set $B$ .
3. Determine the union $A \cup B$ by combining all elements from sets $A$ and $B$ .

STEP 3

Define the set $A$ .
$A = \{ x \mid x \text{ is an odd integer} \} = \{\ldots, -3, -1, 1, 3, \ldots\}$

STEP 4

Define the set $B$ .
$B = \{ x \mid x \text{ is an even integer greater than 0} \} = \{ 2, 4, 6, \ldots \}$

STEP 5

Determine the union $A \cup B$ by combining all elements from sets $A$ and $B$ .
$A \cup B = \{\ldots, -3, -1, 1, 3, \ldots \} \cup \{ 2, 4, 6, \ldots \} = \{\ldots, -3, -1, 1, 2, 3, 4, 6, \ldots \}$
So, the correct answer is: B. $\{\ldots,-3,-1,1,2,3, \ldots\}$

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