# tautology

• Oct 19th 2007, 05:06 PM
rune2402
tautology
Hi! I have a tautology problem for 3 points in my class, but i am not even at the chapter involved. I am a day away. This is the problem:

Is it tautology? Why or why not?
( p ^ q) --> (p V q)

In particular, I as yet do not understand what the arrow represent or how the relation is made between the two statement.

I have to have this figured out by tomorrow. Any help appreciated.
• Oct 19th 2007, 05:45 PM
galactus
This isn't something to start trying to understand the night before.

If you have p \/ q, the only way it's false is when both are false, otherwise, true.

If you have p /\ q, the only way it's true is when both are true, otherwise, false.

p ---> q, the only way it's false is when the antecedent, p, is true and the consequent, q, is false.

Start by building your truth table.

Code:

``` p    q    p /\ q    p \/ q    (p /\ q)--->(p \/ q)   T    T T    F F    T F    F```
There's a start. Now finish 'er up.
• Oct 19th 2007, 05:53 PM
rune2402
Hey thanks. Stuff happens. I really appreciate the help.I'll be back.:)

I undrstand the truth tables and what you said, but what is the arrow suppose to mean.
p q p /\ q p \/ q (p /\ q)--->(p \/ q)

T T T F
T F F T
F T F T
F F T F

I mean I understand the rules for "and" and "or," but I do not see a relation between the statement seperated by the arrow. I don't know what the arrow means.

By the way if the elements p and q are both false then the statement p/\ q is false right?
• Oct 19th 2007, 06:17 PM
galactus
p--->q means p then q. The only way it is false is if p is true and q is false. Go from there. Yes, you are correct about /\. It is true only when both are true. So, if both are false, it's false.