Assume that month is an int variable whose value is 1 or 2 or 3 or 4 or 5 ... or 11 or 12.

Write an expression whose value is "jan" or "feb" or "mar" or "apr" or "may" or "jun" or "jul" or "aug" or "sep" or "oct" or "nov" or "dec" based on the value of month. (So, if the value of month were 4 then the value of the expression would be "apr".)

One possible expression to achieve this is:

```
((month == 1) ? "jan" :
(month == 2) ? "feb" :
(month == 3) ? "mar" :
(month == 4) ? "apr" :
(month == 5) ? "may" :
(month == 6) ? "jun" :
(month == 7) ? "jul" :
(month == 8) ? "aug" :
(month == 9) ? "sep" :
(month == 10) ? "oct" :
(month == 11) ? "nov" :
"dec")
```

In this expression, the ternary operator `? :` is used to check the value of the `month` variable. For each value, a corresponding month abbreviation is assigned as the result.

To get the corresponding month name based on the value of the integer variable "month", you can use a switch statement or an array to map the integer values to the corresponding month names. Here's an example using a switch statement in Java:

```java
String monthName;

switch (month) {
case 1:
monthName = "jan";
break;
case 2:
monthName = "feb";
break;
case 3:
monthName = "mar";
break;
case 4:
monthName = "apr";
break;
case 5:
monthName = "may";
break;
case 6:
monthName = "jun";
break;
case 7:
monthName = "jul";
break;
case 8:
monthName = "aug";
break;
case 9:
monthName = "sep";
break;
case 10:
monthName = "oct";
break;
case 11:
monthName = "nov";
break;
case 12:
monthName = "dec";
break;
default:
monthName = "Invalid month";
break;
}
```

This switch statement will assign the corresponding month name to the "monthName" variable based on the value of the "month" variable.

Alternatively, you can use an array to map the integer values to the month names. Here's an example using an array in Java:

```java
String[] monthNames = {"", "jan", "feb", "mar", "apr", "may", "jun", "jul", "aug", "sep", "oct", "nov", "dec"};

String monthName;

if (month >= 1 && month <= 12) {
monthName = monthNames[month];
} else {
monthName = "Invalid month";
}
```

In this example, the month names are stored in an array, and the array index is used to retrieve the corresponding month name based on the value of the "month" variable.

To evaluate an expression based on the value of the variable `month` and return a corresponding month name, you can use a conditional statement, specifically a switch statement in this case. Here's how you can write the expression in several programming languages:

In Python:

```python
# Assuming the variable month holds the value
# representing the month from 1 to 12

month = 4 # Example value, can be any number from 1 to 12

# Implementing the expression using a dictionary
month_dict = {
1: "jan",
2: "feb",
3: "mar",
4: "apr",
5: "may",
6: "jun",
7: "jul",
8: "aug",
9: "sep",
10: "oct",
11: "nov",
12: "dec",
}

month_name = month_dict.get(month, "Invalid month")

print(month_name) # Output: apr
```

In JavaScript:

```javascript
// Assuming the variable month holds the value
// representing the month from 1 to 12

const month = 4; // Example value, can be any number from 1 to 12

// Implementing the expression using a switch statement
let monthName = "";

switch (month) {
case 1:
monthName = "jan";
break;
case 2:
monthName = "feb";
break;
case 3:
monthName = "mar";
break;
case 4:
monthName = "apr";
break;
case 5:
monthName = "may";
break;
case 6:
monthName = "jun";
break;
case 7:
monthName = "jul";
break;
case 8:
monthName = "aug";
break;
case 9:
monthName = "sep";
break;
case 10:
monthName = "oct";
break;
case 11:
monthName = "nov";
break;
case 12:
monthName = "dec";
break;
default:
monthName = "Invalid month";
break;
}

console.log(monthName); // Output: apr
```

In both cases, the expression first checks the value of `month` and assigns the corresponding month name to the variable `month_name` or `monthName`. If the value of `month` is outside the range of 1 to 12, it assigns the string "Invalid month" to the variable.