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October 9th, 2011, 10:19 AM   #1
 
Joined: Oct 2011

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Simplifying Algebra Proposition

guys i seriously have no idea on how to start this one..

(pVq)^(-pVq)^(pV-q)^(-pV-q)

how to simplify this one?

my teacher gave me this example:

p^(pVq) =- (pVf)^(pVq) <--- how is that f in there??
=- p V (f^q)
=- p V f
=- p

i could just solve this using truth table, but he want me to use
algebra rules. if you guys can help me, i would definitely appreciate
it

thanks alot

im having problem with the rules of algebra being implemented in non numeric arguments.

i did truth table of (pVq)^(-pVq)^(pV-q)^(-pV-q)
and found that the whole proposition is equivalent to (-pV-q)
abang526 is offline  
 
October 9th, 2011, 04:19 PM   #2
 
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Re: Simplifying Algebra Proposition

Quote:
Originally Posted by abang526

my teacher gave me this example:

p^(pVq) =- (pVf)^(pVq) <--- how is that f in there??
=- p V (f^q)
=- p V f
=- p
There is a negation missing in the first line.

Your teacher uses to denote the truth value of a false statement, which he meant a contradiction since a contradicting statement is false.

I assume you know that the truth value of , and of .

If you substitute for , you will get , and of

, see[*]

, see [**]
Quote:
Originally Posted by abang526
guys i seriously have no idea on how to start this one..

(pVq)^(-pVq)^(pV-q)^(-pV-q)

how to simplify this one?
You can rearrange it so that you can get similar terms for contraction. Like this

You do the rest.
Math Dreamer is offline  
October 9th, 2011, 04:59 PM   #3
 
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Re: Simplifying Algebra Proposition

[
((p ^ -p) V q) ^ (p V -q) ^ (-p V -q)
((p ^ -p) V q) ^ ((p ^ -p) V -q)
(F V q) ^ ((p ^ -p) V-q)
= (F V q = q) ^ ( (p ^ -p = F) V -q)
= q ^ (F V -q)
= q ^-q

did i do it right?
abang526 is offline  
October 9th, 2011, 07:45 PM   #4
Math Team
 
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From: Lexington, MA

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Re: Simplifying Algebra Proposition

Hello, abang526!

The statement is a self-contradiction . . . always false.

We need a couple of theorems:

[color=beige]. . [/color]


Quote:



soroban is offline  
October 9th, 2011, 10:32 PM   #5
 
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Re: Simplifying Algebra Proposition

thanks soroban for your explanation..

so anyway, here's something i tried on my own..

(p^-(pV-q)) V q ^ (qVp)
p ^ -p ^ q V q <- ( q ^ q V p = q right? )
f ^ q V q
f V q
T

is it correct? thanks
abang526 is offline  
October 10th, 2011, 01:52 AM   #6
 
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Re: Simplifying Algebra Proposition

i dont mean to keep asking here, i do get the ideas but the methods are somehow different.. im totally lost on how to do the next one..

(p V ( -q -> p)) V ((p <-> -q) -> (q ^ -p))

(p ^ (q -> -r)) V ((-p V r) <-> -q)
(p ^ q) -> ( p ^ -r) V ((-p V -q) <-> ( r V -q)) <- does it work like this?

thanks a lot!!
abang526 is offline  
September 29th, 2013, 03:42 AM   #7
 
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Re: Simplifying Algebra Proposition

how to simplyfy this?
(p'^q)\/('(p^q')^(p\/q'))
T.M.Hanshinie is offline  
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