Conditional Proofs
1. P>Q
2. R>Q
conclusion is (PvR)>Q
To prove the conclusion (PvR) > Q using a conditional proof, we need to assume (PvR) as a temporary assumption and then derive Q from it. Here's the step-by-step explanation on how to approach this proof:
1. Assume (PvR) as a temporary assumption.
2. Based on the assumption (PvR), we have two cases to consider:
a. Assume P as a sub-assumption.
- From the main assumption (PvR), we can derive P by using the disjunction elimination rule (vE).
- Using the assumed P and the given premise P > Q, we can derive Q using the conditional elimination rule (->E).
b. Assume R as a sub-assumption.
- From the main assumption (PvR), we can derive R by using the disjunction elimination rule (vE).
- Using the assumed R and the given premise R > Q, we can derive Q using the conditional elimination rule (->E).
3. Since we have derived Q in both cases, we can conclude that Q follows from the assumption (PvR) by using the disjunction elimination rule (vE).
Therefore, we have proven (PvR) > Q using a conditional proof.