# 辅导MATH1090程序、辅导Python，c++编程

 辅导MATH1090程序、辅导Python，c++编程 MATH1090 Problem Set No2 October 2021 Lassonde School of Engineering Dept. of EECS Professor G. Tourlakis MATH1090 B. Problem Set No2 Posted: Oct. 6, 2021 Due: Oct. 29, 2021; by 2:00pm, in eClass. Q: How do I submit? A: (1) Submission must be a SINGLE standalone file to eClass. Submission by email is not accepted. (2) Accepted File Types: PNG, JPEG, PDF, RTF, MS WORD, OPEN OFFICE, ZIP (3) Deadline is strict, electronically limited. (4) MAXIMUM file size = 10MB Post’s Theorem use is not allowed in any question below. 1. (3 MARKS) We proved in class that ` A ≡ A Page 1 G. Tourlakis MATH1090 Problem Set No2 October 2021 using the “trick” of a Leibniz “mouth”-variable p that does not appear in A. Prove this again, Equationally, but without using this trick and without using Post’s Theorem. 2. (5 MARKS) Prove Equationally that A, B ` A ≡ B. 3. (5 MARKS) Is Statement (1) below True or False and WHY? Γ ` A≡B is equivalent to “Γ ` A IFF Γ ` B” (1) 4. (5 MARKS) Prove Equationally that for any A and B A, ¬A ` B ≡ ¬B 5. (4 MARKS) Prove Equationally that ` A → B → A. 6. (4 MARKS) Prove Equationally that A → B ` ¬B → ¬A. 7. (5 MARKS) Prove (choose your favourite: Equational or Hilbert proof) that A → B ` (B → C) → A → C. 8. Prove that A → B, C → B ` (A ∨ C) → B. two proofs are required: • (3 MARKS) One with the Deduction theorem (and a Hilbert-style proof; CUT rule allowed in this subquestion). • (4 MARKS) One Equational, WITHOUT using the Deduction theorem. Page 2 G. Tourlakis   http://www.daixie0.com/contents/3/6287.html
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