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# Completely lost - Prop Calc watch

1. Ok can someone just point me in the right direction, because I have no idea how to even start this question (what is it even asking me to do?!?!?)

Show that every truth table in two variables is the truth table of some formulae in propositional calculus (Hint: 16/2 = 8)

2. (Original post by Ewan)
Ok can someone just point me in the right direction, because I have no idea how to even start this question (what is it even asking me to do?!?!?)

Show that every truth table in two variables is the truth table of some formulae in propositional calculus (Hint: 16/2 = 8)

There are 16 truth tables of two variables (why?) such as the one below:

P Q
T T T
T F T
F T F
F F T

Can you write down a statement involving P and Q that yields that true table?

You in the end will only have to do 8. Having done the one above you can use its negation automatically to do the FFTF table.
3. Pv~Q,

K I see, cheers dude, so I have for instance

TTT
TTF
TFT
FTT ..... etc... 16 combinations of arranging in two variables... then I need to find the corresponding equation in prop calc... is there any easyway of doing this? Or i just experiment with outcomes to prop calc equations
4. (Original post by Ewan)
Pv~Q,

K I see, cheers dude, so I have for instance

TTT
TTF
TFT
FTT ..... etc... 16 combinations of arranging in two variables... then I need to find the corresponding equation in prop calc... is there any easyway of doing this? Or i just experiment with outcomes to prop calc equations
Just experiment. There won't be just one formula for each table. Other tautological formula will work (like Q implies P) for the one I gave you.
5. I've never heard the term 'prop calculus' but would this not have something to do with factorials?
6. (Original post by RichE)
Just experiment. There won't be just one formula for each table. Other tautological formula will work (like Q implies P) for the one I gave you.
I only need to find one equation for each truth table though right? Not all possible equations.
7. (Original post by Ewan)
I only need to find one equation for each truth table though right? Not all possible equations.
Yes, just one - there will be infinitely many logical formulae that give each table

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