[15 marks, 5 marks each] Use the Hilbert-style method ONLY to prove the following: (Note: do not use the deduction theo...
1. [15 marks, 5 marks each] Use the Hilbert-style method ONLY to prove the following: (Note: do not use the deduction theorem. Do not use Post's theorem. Do not use Equational-Style proof) 1. [15 marks, 5 marks each] Use the Hilbert-style method ONLY to prove the following: (Note: do not use the deduction theorem. Do not use Post's theorem. Do not use Equational-Style proof)
[15 marks, 5 marks each] Use the Equational-style method ONLY to prove the following: (Note: do not use the deduction theorem. Do not use Post's theorem. Do not use Hilbert-Style proof) 2. b. FA> (В > C) %3D (А — В) > (А — С) с. А > ВЕСVA —CVВ [15 marks, 5 marks each] Use the Equational-style method ONLY to prove the following: (Note: do not use the deduction theorem. Do not use Post's theorem. Do not use Hilbert-Style...
[5 marks, 2, 3 marks respectivelyl Use the deduction theorem and resolution (but NOT Post's theorem) to prove the following: 3. [5 marks, 2, 3 marks respectivelyl Use the deduction theorem and resolution (but NOT Post's theorem) to prove the following: 3.
3. [5 marks, 2, 3 marks respectively] Use the deduction theorem and resolution (but NOT Post's theorem) to prove the following: (A B) A - B) > A а. F (Ал-В) (AB b. H 3. [5 marks, 2, 3 marks respectively] Use the deduction theorem and resolution (but NOT Post's theorem) to prove the following: (A B) A - B) > A а. F (Ал-В) (AB b. H
Use the method of direct proof to prove the following statement: For integers a and b, if a is odd or b is odd, then (a + 7)(b 5) is even.
4. (5 points) Use the substitution method to prove the guess that is indeed correct when T(n) is defined by the following recurrence relations: T(n) = 3T(n/3) +5; T(1) = 5. At the end of your proof state the value of constant c that is needed to make the proof work. Statement of what you have to prove: Base Case proof: Inductive Hypotheses: Inductive Step: Value of c: 5. (6 points) Find a counterexample to the following claim: f(n)=O(s(n)) and...
Part I: Induction (90 pt.) (90 pt., 15 pt. each) Prove each of the following statements using induction, strong induction, or structural induction. For each statement, answer the following questions. a. (3 pt.) Complete the basis step of the proof. b. (3 pt.) What is the inductive hypothesis? c. (3 pt.) What do you need to show in the inductive step of the proof? d. (6 pt.) Complete the inductive step of the proof. 5. Let bo, bu, b2,... be...
5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M > M is a TM and 1011 E L(M)}.
prove each of the following theorems using weak induction 1 Weak Induction Prove each of the following theorems using weak induction. Theorem 1. an = 10.4" is a closed form for an = 4an-1 with ao = 10. Theorem 2. an = (-3)"-1.15 is a closed form for an = -3an-1 with a1 = 15. Theorem 3. In E NU{0}, D, 21 = 2n+1 -1. Theorem 4. Vn e N, 2" <2n+1 - 2n-1 – 1. Theorem 5. In E...
For each of the following pairs of sets, prove that they are equinumerous. Remember that we have two ways to do this: we can find a bijection explicitly, or we can prove that there is an injection in each direction and then use the Schr¨oder-Bernstein theorem. 4. N and Qd for d > 1 5. R and R x R {a + bi |2 =-1, a,bE R} is the complex numbers) 6. R and C (where C