4

```
I will pass the exam or I will not pass the exam.
If I will pass the exam, then I will pass the exam even if I don't study.
If I will pass the exam even if I don't study, then studying is pointless.
If I will not pass the exam, then I will not pass the exam even if I study.
If I will not pass the exam even if I study, then studying is pointless.
Therefore, studying is pointless.
```

I pass the exam : A

I study : B

Studying is pointless: C

A v ~A

A → (~B → A)

(~B → A) → C

~A → (B → ~A)

(B → ~A) → C

C

```
+---+----+----------------+----------------+-----+
| A | B | (~B → A) → C V (B → ~A) → C | C |
+---+----+----------------+----------------+-----+
| 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 1 |
+---+----+----------------+----------------+-----+
```

I'm not sure how to put this argument into a truth-table (I tried; maybe there are 8 rows instead of 4?) and would appreciate it if someone showed me the correct form. Please tell me whether the following statements which I came up with are correct:

Premises 1,2 and 4 are tautologous.

The argument is valid.

The argument is unsound as premises 3 and 5 are untrue. Can I say something like how you would learn stuff by studying even if you fail the exam?

I'm doing computer science and I'm trying to learn some logic as it's helpful there. Thanks for the help!

Hint: Your statement list can be rewritten as

`(A v ~A) ^ (A -> (~B -> A)) ^... -> C`

(I'd recommend reducing before putting it into a truth table). In terms of arguments against, this doesn't take into account the situation in which if you do study you pass (`B -> A`

). – IllusiveBrian – 2016-02-26T21:55:37.370Yes; if you want to use truth table, you have to build it for all the sentential letters involved: A,B,C and thus eight rows. The argument is

validif the conclusion has 1 (TRUE) in every row whereallthe premises have 1, i.e. in every case where all the premises are TRUE also the conclusion is. – Mauro ALLEGRANZA – 2016-02-27T08:56:36.363For the truth-table, it would have to be 8 rows, with other headings such as "A ^ ~B", "~A ^ B" and "[(A ^ ~B) v (~A ^ B)] → C" (this one is the conclusion). Is this correct? – Chthonic Zyceus – 2016-02-27T12:43:31.057