Logical disjunction elimination rule I know these two rules about disjunctive introduction (Vi (1), Vi (2)).

In other words: Given p I can deduct p V q
But this rule of disjunctive elimination

Is that the same as saying the "reverse" of the first two?
That is, given p V q can I get both p and q using Ve
Sorry if I'm unclear!
 A: Not really. After all, you shouldn't expect to be able to derive components from an 'or' statement: after all 'TRUE or FALSE' is true, but you can only possibly derive 'TRUE' as a true statement. You can't possibly prove 'FALSE'.
This rule is, indeed, one of the trickiest to understand. This is because it doesn't just take statements as its inputs. Instead, two of the inputs - the large vertical boxes in the rule - are entire proofs. If you have '$p \vee q$' and a proof that assuming $p$ you can conclude $\chi$ and a proof that assuming $q$ you can conclude $\chi$... then from all three of these things - the disjunction and the two proofs - you can conclude $\chi$.
This rule might be easier to appreciate if you look at it from the viewpoint of how we might naturally prove things, where it looks exactly like a proof by cases:


*

*"I know that either Case A or Case B holds."

*"In Case A, I can show $\chi$."

*"In Case B, I can show $\chi$."

*"Therefore $\chi$ holds in all cases. $\chi$ is always true."


The disjunction elimination rule is just the formalisation of this sort of argument. 
