Write each of the following sets in Roster form and write the cardinal number of each .
A= { x: x is an integer , - 3 < x `le` 4}

Answer

To solve the problem, we need to express the set A in roster form and determine its cardinal number. Let's break this down step by step.

### Step 1: Understand the Set Definition
The set A is defined as:
\[ A = \{ x : x \text{ is an integer}, -3 < x \leq 4 \} \]
This means we are looking for all integer values of \( x \) that are greater than -3 and less than or equal to 4.

### Step 2: Identify the Range of Integers
We need to find all integers that satisfy the condition:
- The integer \( x \) must be greater than -3 (so -3 is not included).
- The integer \( x \) must be less than or equal to 4 (so 4 is included).

### Step 3: List the Integers in the Range
Starting from the smallest integer greater than -3, we have:
- The first integer greater than -3 is -2.
- Continuing, the integers are: -2, -1, 0, 1, 2, 3, and 4.

### Step 4: Write the Set in Roster Form
Now we can write the set A in roster form:
\[ A = \{-2, -1, 0, 1, 2, 3, 4\} \]

### Step 5: Count the Elements in the Set
Next, we need to determine the cardinal number of the set A, which is the number of elements in the set. We can count the elements:
- The elements are: -2, -1, 0, 1, 2, 3, 4.
- There are a total of 7 elements.

### Step 6: Write the Cardinal Number
Thus, the cardinal number of set A is:
\[ n(A) = 7 \]

### Final Answer
The set A in roster form is:
\[ A = \{-2, -1, 0, 1, 2, 3, 4\} \]
The cardinal number of set A is:
\[ n(A) = 7 \]

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