# Homework Help: Help, using Truth Table prove that the following logic statement is a Tautology

1. Aug 30, 2010

### Tek1Atom

1. The problem statement, all variables and given/known data

By providing a truth table, show that the following logic statement is a tautology:

p ∧ (p → q) → q

Any help will be much appreciated.

Thank You

2. Aug 30, 2010

### Staff: Mentor

I would set up a truth table with columns for p, q, and p ==> q. You know how many rows you need, right?

3. Aug 30, 2010

### Tek1Atom

p | q | P → q
-------------
T | T | T
T | F | F
F | T | T
F | F | T

Thank you Mark44 but I don't think this is the correct answer/method as the output has to be true in all cases in order for it to be labeled a tautology. Any other suggestions?

4. Aug 30, 2010

### D H

Staff Emeritus
You are missing at least one column, multiple columns if you want to break things down.

5. Aug 30, 2010

### Tek1Atom

D H could you give me an example please as I am new to logic...

6. Aug 30, 2010

### D H

Staff Emeritus
You have the truth table for implication. p→q obviously is not a tautology. You weren't asked to show that. You were asked to show that p∧(p→q)→q is a tautology. Your truth table needs to end with a p∧(p→q)→q column on the right and with all four values in this column being T.

7. Aug 31, 2010

### Tek1Atom

Thank you DH, that was very helpful. My final question is, does it matter which way we write down the truth table?

e.g.

which one is correct?

p | q | P → q | p∧(p→q)→q
---------------------------
T | T | T | T
T | F | F | T
F | T | T | T
F | F | T | T

OR

p | q | P → q | p∧(p→q)→q
---------------------------
F | F | T | T
F | T | T | T
T | F | F | T
T | T | T | T

8. Aug 31, 2010

### D H

Staff Emeritus
You aren't going to get points for that. At least I hope you aren't. There is a thing called showing your work.

9. Aug 31, 2010

### Staff: Mentor

To answer your question about the order, it doesn't really matter, but these are usually presented with the top row being T T ... and the bottom row being F F ...

10. Aug 31, 2010

### Tek1Atom

Thank You Mark44. You have been great!