1. ## [SOLVED] logic proof

by using the rules of inference how can I prove that:

(AvB)n(AvC) concludes Av(BnC)

I know how to prove it the other way round using rules of inference but when i try to prove it this way I get stuck. Here is my work:

1 (AvB)n(AvC) hypothesis
2 (AvB) n-elimination on line 1

3 A Assumption
4 Av(BnC) v-introduction on line 3

5 B Assumption

I don't know how to continue this proof using rules of inference. Any help appreciated.
thanks.

2. ## truth table

you cannot use a truth table?

I assume the n is representing the 'and' sign, right?

3. Try using de Morgan's law.
$\displaystyle \neg (p\vee q)\leftrightarrow \neg p\wedge \neg q$
Thus,
$\displaystyle \neg [(A \vee B)\wedge (A \vee C)]$
becomes,
$\displaystyle \neg (A \vee B) \vee \neg (A \vee C)$
That is the form of using the law of inference.