Questions: Express the set using the roster method. [ x mid x in N text and x<4 ] Choose the correct answer below. A. 1,2,3 B. 0,1,2,3 C. 1,2,3,4 D. ...,-3,-2,-1,0,1,2,3,4

Express the set using the roster method. [ x mid x in N text and x<4 ] Choose the correct answer below. A. 1,2,3 B. 0,1,2,3 C. 1,2,3,4 D. ...,-3,-2,-1,0,1,2,3,4
Transcript text: Express the set using the roster method. \[ \{x \mid x \in N \text { and } x<4\} \] Choose the correct answer below. A. $\{1,2,3\}$ B. $\{0,1,2,3\}$ C. $\{1,2,3,4\}$ D. $\{\ldots,-3,-2,-1,0,1,2,3,4\}$
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Solution

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Solution Steps

Step 1: Identify the Set Definition

The set is defined as \( \{x \mid x \in N \text{ and } x < 4\} \). This means we are looking for all natural numbers \( x \) that are less than 4.

Step 2: Determine the Natural Numbers Less Than 4

Natural numbers \( N \) typically start from 1. Therefore, the natural numbers less than 4 are \( 1, 2, \) and \( 3 \).

Step 3: Match the Set with the Given Options

The set \( \{1, 2, 3\} \) corresponds to option A. The other options either include numbers outside the natural numbers or include 0 or 4, which do not satisfy the condition \( x < 4 \).

Step 4: Conclusion

The correct answer is option A.

Final Answer

The correct answer is A.

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