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Give natural deduction proofs for the following sequents (4 points each): P , P --> Q , Q --> T P T ( A B

Give natural deduction proofs for the following sequents (4 points each):

  1. P, P --> Q, Q --> T P T
  2. (A B) --> C A --> (B --> C)
  3. P Q, Q -->? T P -->T
  4. A -->(B -->C) (A B ) -->C
  5. P --> S, Q -->S, Q -->T (P Q) --> (S T)

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