Give a proof to show that for any wffs A,B:
(∃x)A→(∀x)B⊢(∀x)(A→B)
Please give like and commet
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Give a proof to show that for any wffs A, B: (3x)(A A (V)B) F (x)B.
give a proof by contradiction. there does not exist any rational number x such that x * sqrt(2) = sqrt(3)
Give a proof to show: (∀x)x=f(x,y),(∀x)φ(x,x)⊢(∀x)(x=f(x,y)∧φ(x,x))
Give a proof or counterexample, whichever is appropriate. 1. For any sets A and B, (A ∩ B = ∅) AND (A ∪ B = B) ⇒ A = ∅ 2. An integer n is even if n2 + 1 is odd. 3. The converse of the assertion in exercise 62 is false. 4. For all integers n, the integer n2 + 5n + 7 must be positive. 1.65. For all integers n, the integer n4 + 2n2 − 2n...
4. In this problem, you will give an algebraic proof of the triangle inequality. (a) Show that for any w, z EC, \w + zl2 = ww + (wz + wz) + zz (b) Show that 2Re(wz) < |w|. (c) Use the results of (a) and (b) to prove that [w + zl2 = ([w+ -12 and note how the triangle inequality follows from this one.
proof that
Question 2: Let X and Y be any two random variables and let a and b be any two real numbers. Show that Var(aX +bY) = a? Var(X) + b2 Var(Y) + 2 abCov(X,Y).
(a) Prove that l-x」=-[al and「-2] =- (b) Give a proof by cases that 142] = 1x1+ 1xH + 1x-si + 1x+1 . 3
3. Let f be a continuous function on [a, b] with f(a)0< f(b). (a) The proof of Theorem 7-1 showed that there is a smallest x in [a, bl with f(x)0. If there is more than one x in [a, b] with f(x)0, is there necessarily a second smallest? Show that there is a largest x in [a, b] with f(x) -0. (Try to give an easy proof by considering a new function closely related to f.) b) The proof...
Give Hilbert Style proof of: ⊢ A ∨ A ∧ B ≡ ¬A ∨ B?
Problem 4 (2pts) Let A, B be formulas B) (-AV B) Give a formal proof for the formula (A Give a formal proof for the formula -(-A) A.
Problem 4 (2pts) Let A, B be formulas B) (-AV B) Give a formal proof for the formula (A Give a formal proof for the formula -(-A) A.