I have a question is about proving a argument is valid or not. Again, cannot really understand the solution.
The question is like this
Determine if the following arguments are valid.
- It is not the case that IBM or Xerox will take over the copier market. If RCA returns to >the computer market, then IBM will take over the copier market. Hence, RCA will not return >to the computer market.
The solution is like this.
Let a denote “IBM will take over the copier market”, x “Xerox will take the copier market”, r “RCA returns to the computer market”. Then we have the following argument:
$\lnot(a\lor x)$ ${r \rightarrow a}\over {so \quad \lnot r }$
- $\lnot (a \lor x)$ $\quad$ premise
- $\lnot a \land \lnot x$ $\quad$ from 1
- $\lnot a$ $\quad$ from 2
- $r \rightarrow a$ $\quad$ premise
- $\lnot a \rightarrow \lnot r$ $\quad$ from 4
- $\lnot r$ $\quad$ from 3 and 5
and the statment is valid
Why the step 2 can go to step 3? Obviously, "It is not the case that IBM or Xerox will take over the copier market" is not equal to "It is not the case that IBM take over the copier market".