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## Homework Statement

Every sentence has a truth-table which can describe it, does every truth table have a sentence?

We're dealing with the SD and SD+ logic derivations.

## Homework Equations

N/A

## The Attempt at a Solution

It's an extra credit question, and isn't really based in any particular chapter, so I'm having trouble on where to look for the answer. My gut says yes, but I'm led to believe otherwise. For any two variables, by using the four main connectives with or without the negation modifier:

Code:

```
[U]A | B | A&B | AvB | A>B | A=B |[/U]
T | T | T | T | T | T |
T | F | F | T | F | F |
F | T | F | T | T | F |
F | F | F | F | T | F |
```

So with those 4 main connectives, each row has one possible outcome. Using those four connectives, each possible combonation for a row (TTTT, TTTF, TTFT, TFTT, ..., TFFF, FFFF) CANNOT be achieved (see FFFT, for example), even by using the negation modifier (~). Does this mean I have proved that every truth table does not have a sentence to go along with it?

But I have no clue what I'm doing, and I think I'm looking at this the wrong way. Any insight?

Thanks.