This is what I did first(Given) A ∧ (B ∨ C)
(To Prove) (A ∧ B) ∨ (A ∧ C)
I have no idea how to make both sub proof same
I got it but I don't understand the logic behind it.
logicpropositional-calculus
This is what I did first(Given) A ∧ (B ∨ C)
(To Prove) (A ∧ B) ∨ (A ∧ C)
I have no idea how to make both sub proof same
I got it but I don't understand the logic behind it.
Best Answer
Several things go wrong here.
First and foremost, there is no need to start any subproofs with $A$ and $B \lor C$, since you can just infer those from the premise using $\land $ Elim
So, start with:
Second, make sure that you get the same line at the end of each subproof before applying $\lor$ Elim, so it'll look like this:
I'll let you figure out what that 'mystery' statement $Q$ should be ... but here's a hint: what statement would like like to have when all is said and done?
Finally, make sure you get $A \land C$, rather than $C \land A$ like you have on line 8. ... and of course get the disjuncts of the desired disjunction in the right order as well