As mentioned in the question I am providing the answer of 2)(b) considering the other two parts are already solved.
Do only b) 2. 9 marks] (Vx)(Vx)A = (Vx)A a) 3 marks] Prove that (Vx)(Vx)A =...
[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...
a) Prove that \(\vdash(\forall x)(\forall x) \mathrm{A} \equiv(\forall x) \mathrm{A}\)b) State the dual of \(\vdash(\forall x)(\forall x) \mathrm{A} \equiv(\forall x) \mathrm{A}\)c) Prove the dual theorem you stated in b)
[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) 1.
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)
[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.
[10 marks] Prove using the rules of inference that the premise Vx((W(x) v B(x)) A(W(x) B(x))) implies the conclusion Vx (-W(x)B(x))
2 (b) Prove that + 3 cos(atx) O has at least two solutions with x € (-1,1]. [20 Marks] 1 + x2 (c) State the Rolle's Theorem. [5 Marks] (d) Prove that + 3 cos(1x) = 0 has excalty one solution in [0, 1]. 1 + x2 [20 Marks (Hint:Use proof by contradiction, by supposing more than one root. ]
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
(5 marks Consider the following general linear program (P). max{c Ar = b, x 2 0}. пax- (a) Write down the dual (D) of this linear program. (b) Prove the Weak Duality Theorem directly for this particular (P) and (D)
3 marks] Question 9 a) Write the expression for the self-ionization of water [2 marks] b) State the pkw value for pure water at 25°C (2 marks] c) Describe how the concentration of ions changes if an acid were to be added to the water (4 marks] Question 10 What is the pH of a solution formed by mixing 125.0 ml of 0.0250M HCl with 75.0 ml of 0.0500M NaOH? March 2o1g Version 1.0. 14