Find the cardinal number of set C=x 25<x<40, x ∈

Questions: Find the cardinal number of set C=x 25<x<40, x ∈ Z, where Z denotes the set containing all integers.

Transcript text: 333 > Assignments > Week 1: Set Fundamentals Week 1: Set Fundamentals Due Sunday by 11:59pm Points 10 Submitting an external tool Identify the cardinal number for a set Question Find the cardinal number of set \[ C=\{x \mid 25

Solution

Solution Steps

To find the cardinal number of the set \( C = \{x \mid 25 < x < 40, x \in \mathbb{Z}\} \), we need to determine how many integers satisfy the condition \( 25 < x < 40 \). This involves listing all integers between 26 and 39 inclusive and counting them.

Step 1: Define the Set

We define the set \( C \) as follows: \[ C = \{ x \mid 25 < x < 40, x \in \mathbb{Z} \} \] This means \( C \) includes all integers \( x \) such that \( 25 < x < 40 \).

Step 2: Identify the Elements of the Set

The integers that satisfy the condition \( 25 < x < 40 \) are: \[ C = \{ 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 \} \]

Step 3: Calculate the Cardinal Number

To find the cardinal number of the set \( C \), we count the number of elements in \( C \): \[ \text{Cardinal Number} = |C| = 14 \]