Can someone help me with those two argument problems? No matter how many times I try I reach a dead end at some point. These problems require the proof laws to show if the arguments are valid or not.

1- If the rat ate the cheese or the rate is not in the trap, then it is under the bed.

The Rat is neither under the bed nor under the table. You will see the Rat footprint unless It is under the table or it is not in the trap. The Rat did drink the water if you see its footprint. The rate ate the cheese or it did not eat the newspaper. Therefore if the rate neither under the table nor under the bed, then It did not eat the newspaper but it drank the water.

2-

And this one's seemed easy so I managed to figure out it's valid, but I just wanna check with you guys. I came up with the answer because it's not possible to make the premises all true while setting the conclusion to false, well you can do it with a truth table as well and get the answer.

Any kind of help is appreciated.