Discreet Structure/Math Problems- Proving and Propositional Statement Questions

Proof the following:

1. (A'->B') ^ (A->C) -> (B->C)

2. (Y->Z') ^ (X'->Y) ^ [Y->(X->W)] ^ (Y->Z) -> (Y->W)

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The crop is good, but there is not enough water. If there is a lot of rain or not a lot of sun, then there is enough water. Therefore the crop is good and there is a lot of sun. (use letters C, W, R, S)

If the program is efficient, it executes quickly. Either the program is efficient, or it has a bug. However, the program does not execute quickly. Therefore it has a bug. (use letters E, Q, B)

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Write down the propositional form of the following argument:

If my client is guilty, then the knife was in the drawer. Either the knife was not in the drawer or Jason Pritchard saw the knife. If the knife was not there on October 10, it follows that Jason Pritchard didnt see the knife. Furthermore, if the knife was there on October 10, then the knife was in the drawer and also the hammer was in the barn. But we all know that the hammer was not in the barn. Therefore, ladies and gentlemen of the jury, my client is innocent.