A. Symbolize the following sentences into propositional logic form...

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A. Symbolize the following sentences into propositional logic formulas. Each symbolization is worth 2 points.
1. Provided that the MONEY is deposited, the LENDER will get the payment if the WIRE goes through
2. PASSING the background check is a necessary condition for getting HIRED.
3. The process is GUARANTEED only if payment is RECEIVED.
4. The game was WON, and the team will CELEBRATE if they have TIME.
5. If MARVIN is ill, then JUAN will get the medicine and the DOCTOR will prescribe B. Construct proofs for the following sequents. Even if you do not feel that you can get to the conclusion, try to do as many lines as you can since you will be given some points for attempting to do the proof. Each one is worth 16 points.

1. A→B ├   A→(A&B)

2. A→(B→C)├ (B&A)→C

3. D → T, (D & T) → F ├ D → F

4. D&C, (C&D) → (A&B) ├ A   

5. A&B, (A→R)&(B→S) ├ R&S

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