CONSTRUCT A FORMAL PROOF FOR THE ARGUMENT USING THE INDIRECT METHOD

For the conclusion to be F, a is F and p is T

this would make both the first and second premises F

therefore the argument is valid by 'the method of backward fell swoop' .

Correction
Putting a=F and p=T makes the conjunction of the premises F, hence the argument is valid by backward fell,swoop.

What's a backward fell swoop, please ?

See my reply on other thread.

This argument form leaves out the possibility ~c. That is, indirect proof is not valid under the following conditions: if a number of pre-conditions are necessary for a result to be true, and the result is not true, any of the pre-conditions can be false. It is only legitemate if you assume that all c -> p has been established. Normally, the method is used to point out, you either have to give up a or you have to give up a causal relationship that you are unlikely to be willing to abandoned. This is not to attack the method itself, it is an extremely valuable tool. And it can be valid when arguing carefully from a set of explicitly stated axioms. However, this is not the way it is normally used and the presumed validity should be recognized.

Not sure what you mean here. The truth value of c is irrelevent to the proof. If in doubt construct the truth table.