Can someone help me construct this truth table? P->(P ->(Q ^ P)). Now, does this mean that first, you work the Q^P? or do you work the p-> which is inside the ( ) first. Then do you take the result of whichever is used and connect it with p-> which is oustide the ( ). Do that make sense. I'm confused too.
Start with this:
P|Q| P->(P ->(Q ^ P))
T|T|
T|F|
F|T|
F|F|
Now transfer TTFF under every P, and TFTF under every Q
P|Q| P->(P ->(Q ^ P))
T|T| T T T T
T|F| T T F T
F|T| F F T F
F|F| F F F F
Now take care of the ^, because that's the innermost
operation. If ^ is between two T's it's T, otherwise it's F
So we use this rule to fill in under the ^, but everytime
we do we scratch through the letters on each side of it,
like this:
P|Q| P->(P ->(Q ^ P))
T|T| T T T T T
T|F| T T F F T
F|T| F F T F F
F|F| F F F F F
Now I'll just erase them, but you can just leave them
scratched:
P|Q| P->(P ->(Q ^ P))
T|T| T T T
T|F| T T F
F|T| F F F
F|F| F F F
Now take care of the second ->, because that's now the innermost
operation. If -> has a T on the left and an F on the right,
then it's F, otherwise it's T. So we use this rule to fill
in under the ->, but as before, every time we do we scratch
through the letters on each side of it, like this:
P|Q| P->(P ->(Q ^ P))
T|T| T T T T
T|F| T T F F
F|T| F F T F
F|F| F F T F
Again I'll erase the ones scratched, but you can just leave them
scratched:
P|Q| P->(P ->(Q ^ P))
T|T| T T
T|F| T F
F|T| F T
F|F| F T
Finally we take care of the first ->, because that's now
the innermost operation. We use the same rule again to fill
in under the first ->,
P|Q| P->(P ->(Q ^ P))
T|T| T T T
T|F| T F F
F|T| F T T
F|F| F T T
And erasing those marked thru:
P|Q| P->(P ->(Q ^ P))
T|T| T
T|F| F
F|T| T
F|F| T
Edwin