Questions: C = z12 ≤ z ≤ 34 and z is a multiple of 3

Transcript text: C = \{z|12 \leq z \leq 34 \text{ and } z \text{ is a multiple of } 3\}

Solution

Solution Steps

To solve this problem, we need to find all integers \( z \) that satisfy two conditions: they must be between 12 and 34 inclusive, and they must be multiples of 3. We can achieve this by iterating through the range from 12 to 34 and checking if each number is divisible by 3.

Step 1: Define the Set \( C \)

We are tasked with finding the set \( C \) defined as: \[ C = \{ z \mid 12 \leq z \leq 34 \text{ and } z \text{ is a multiple of } 3 \} \]

Step 2: Identify Multiples of 3

To find the elements of set \( C \), we need to identify all integers \( z \) within the range from 12 to 34 that are multiples of 3. The multiples of 3 can be expressed as \( z = 3k \) for integers \( k \).

Step 3: List the Elements of Set \( C \)

By checking each integer in the range, we find the following multiples of 3: \[ C = \{ 12, 15, 18, 21, 24, 27, 30, 33 \} \]