
[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) nelimination on line 1
3 A Assumption
4 Av(BnC) vintroduction on line 3
5 B Assumption
I don't know how to continue this proof using rules of inference. Any help appreciated.
thanks.

truth table
you cannot use a truth table?
I assume the n is representing the 'and' sign, right?

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.