Help with logic proof (this should be really basic)

[jamo_]

help with logic proof (this "should" be really basic)

Hey I am new to logic (I've just started a masters)

I can't for the life of me prove this using only the natural deduction inference rules:

A --> B |- ¬A v B

I can do it easily in the other direction but I cannot do it in the above direction.

It's annoying as I can do it easily using truth tables!

Any help much appreciated.

Thanks.

 

[lippyka]

Here is a proof using the Natural Deduction inference rules:1. A → B (Premise)2. ¬A (Assume)3. B (From 1, 2 by Modus Ponens)4. ¬A v B (From 2, 3 by Disjunction Introduction)5. ∴ ¬A v B (From 4 by Reiteration of Assumption)