Show that if p is a positive prime and p = 1 (mod 3), then p...

 

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Show that if p is a positive prime and p = 1 (mod 3), then p = 1 (mod 6). (a) Using only the 16 natural deduction rules prove: P(x,y)→ Vy³xP(x,y) Note: There is indeed no premise given for this natural deduction. (b) Now, write a word proof for the proposition: ArvyP(x,y) → Vyx P(x, y) (c) Prove or disprove its converse. That is, prove or disprove: VyrP(x,y) →rvyP(x, y) Show that if p is a positive prime and p = 1 (mod 3), then p = 1 (mod 6). (a) Using only the 16 natural deduction rules prove: P(x,y)→ Vy³xP(x,y) Note: There is indeed no premise given for this natural deduction. (b) Now, write a word proof for the proposition: ArvyP(x,y) → Vyx P(x, y) (c) Prove or disprove its converse. That is, prove or disprove: VyrP(x,y) →rvyP(x, y)

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The image contains three distinct parts with the initial statement about a mathematical property of prime numbers followed by two statements expecting ... View the full answer