I want to add a new column to my data frame with true and false values to tell me if two columns have duplicated values but the third column has a distinct value.

This is the table I have now:

```
| ID  | name | age|student|
| --- | -----|----|-------|
| 1   | Joe  |23  | Yes   |
| 2   | Rayan|13  | Yes   |
| 3   | Sara |20  | No    |
| 4   | Rayan|21  | Yes   |
| 5   | Sara |20  | Yes   |
| 6   | Joe  |23  | Yes   |

```

I want to check if name and age have duplicated values but student has different value. I want the resulted column to look like this:

```
| ID  | name | age|student|satisfy|
| --- | -----|----|-------|-------|
| 1   | Joe  |23  | Yes   | False |
| 2   | Rayan|13  | Yes   | False |
| 3   | Sara |20  | No    | False |
| 4   | Rayan|21  | Yes   | False |
| 5   | Sara |20  | Yes   | True  |
| 6   | Joe  |23  | Yes   | False |

```

Only Sara satisfies the condition because in age and name have duplicated values but student has different values. How can I do this in R?