[Math] (Given) A ∧ (B ∨ C) (To Prove) (A ∧ B) ∨ (A ∧ C)

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.

Got 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:

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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:

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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

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