Find The Statements And Reasons To This Proof

Premises:

≈P→(Q→≈W)

≈S→Q

≈T

P→T

W→S

Conclusion:

W→S

I don’t really understand how to do this and I have a test coming up so any help would be greatly appreciated.

Solution

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You have W–>S as part of the given premises AND the CONCLUSION we are trying to prove.

I will ignore it.

Since ~T is given and P–>T, then ~P follows by contrapositive.

It follows that Q–>~W per the given premises.

However, ~S –> Q and Q–>~W, so ~S –> Q —> ~W.

Then ~S –> ~W

Therefore W–> S by contra-positive