So you've got
You're asked to prove or disprove .
Since all of your assumptions are implications, the only inference rules you need are modus ponens and modus tollens. In this case, you'd have to assume , and try to show . For modus ponens, you'd need to start somewhere with a on the LHS of an implication. For modus tollens, you'd need to start somewhere with a on the RHS of an implication. That does not occur anywhere in your assumptions. Therefore, I deduce that you're not going to be able to prove . But how do you disprove it? You have to be able to assign truth values to all of the propositions such that all your assumptions are true, and yet is false. In order for to be false, and So now see if you can assign the rest of the truth values of your propositions such that all the assumptions are satisfied. Make sense?