Let M(x) = "x passed the midterm". Let F(x) = "x passed the final". Select the statement below which means: "If nobody passed the midterm, then everyone passed the final" O Vx-M(x)→ VIF(x) Vx(M(x)→-F(x)) +VæM(x) → VF(z) Va( M(x)→ F(x))
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The above question is solved in step 2 :-
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- Let H(x) = " plays hockey". Let B(x) = "x plays basketball". Which statement below means "If Tom plays hockey, then everyone plays basketball." O O O O O H(Tom)→ B(Tom) yH(y) → VxB(x) H(Tom) → VxB(x) H(Tom) V VxB(x) H(Tom) →x B(x)Let p = "Paris is called the City of Lights" and let q = "The Eiffel Tower is locatedin Paris". Write the English statements corresponding to each of the following:(i) ∼p V q(ii) p → q(iii) p V q(iv) ∼p ʌ∼q(v) ∼(p V q).Description Implement a Taylor series approximation of some mathematical functions. In mathematics, the Taylor series is a way of approximating transcendental functions such as sin x or log x. In this approach, we can approximate a mathematical function as closely as we might want to by adding together numbers that get us closer and closer to the true value of the function. For example, the exponential function e" can be approximated as: 73 e" = 1+x + 2! 3! - nl and the sin function can be approximated as: (-1)" 73 sin z = x - 3! „5 77 2n+1 (2n + 1)! 5! 7! n=0 The more terms we include in our approximation, the better an approximation we get of sin x. In this assignment, you must implement Taylor series approximations for these two functions. Your functions should take two parameters: the value of x and the number of terms to use in the approximation: /** * Calculate an approximate value for the exponential function. @param the value to raise e to the power of (i.e., e to the x) *…
- Let B(x) = "x gets a biscotti". Which statements below mean "Either everyone gets a biscotti or no one gets a biscotti"? Select all that apply. Ox B(x) V-3x B(x) Ox B(x) V-Vx B(x) OV (B(x) V-B(x)) 03x B(x) → Vx B(x) 03x B(x) v Vx B(x)Let P(x) = "x passed the class". Let S(x) = "x studied". Let L(x) = "x got lucky". Which statement below means "Everyone who passed the class either studied or got lucky"? OVx ((P(x)→ S(x)) V L(x)) None of the other answer here listed is correct. OVx( P(x)→ S(x)) V L(x) OVx ((S(x) V L(x)) → P(x)) OV (P(x) → (S(x) v L(x)) ) OV (L(x) V (P(x) → S(x)))Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some.. "All funny persons are not friend with Harry" of :
- Give English language translations of the following wffs where L(x, y) is “x loves y”, H(x) is “x ishandsome”, M(x) is “x is a man”, P(x) is “x is pretty”, W(x) is “x is a woman”, k is “Kathy”, andj is “John”.(a) (∀x)(W(x) → (∀y)[L(x, y) → M(y) ∧ H(y)])(b) (∃x)[M(x) ∧ H(x) ∧ L(x, k)](c) (∃x)(W(x) ∧ P(x) ∧ (∀y)[L(x, y) → H(y) ∧ M(y)]) (d) (∀x)[W(x) ∧ P(x) → L(j, x)]I. Let P (x) be the statement “2x = x2 .” If the domain consists of the integers, what are the truth values? a) P(0) b) P(1) c) P(2) d) P(−1) e) ∃x P(x) f ) ∀x P(x) 2. Let Q(x) be the statement “x > x - 1.” If the domain consists of all integers, what are the truth values? a) Q(10) b) Q(−2) c) Q(999) d) ∃x Q(x) e) ∀x Q(x) f) ∃x ˺Q(x) g) ∀x ˺Q(x)Let the following statements be given. p= "You can vote." q = "You are under 18 years old." r = "You are from Mars." (a) Translate the following statement into symbols of formal logic. You can't vote if you are under 18 years old or you are from Mars. O (q vr) → p O¬p → (q^r) O (q^r) → p O (qvr) → p O¬p → (qVr) (b) Give the contrapositive of this statement in the symbols of formal logic. Op (q^r) O¬¬p → ¬(q V r) O¬p → ¬(q Vr) (q V r) → O(g ^r) → p p (c) Give the contrapositive in English. O If you are under 18, then you can't vote nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can't vote. O If you can't vote, then you are not under 18 nor are you from Mars. O If you can vote, then you are not under 18 nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can vote.
- Correct answer will be upvoted else downvoted. Computer science. Michael is blamed for disregarding the social removing rules and making a danger of spreading Covid. He is currently shipped off jail. Fortunately, Michael knows precisely what the jail resembles from within, particularly since it's actual straightforward. The jail can be addressed as a square shape a×b which is separated into stomach muscle cells, each addressing a jail cell, normal sides being the dividers among cells, and sides on the border being the dividers prompting opportunity. Prior to condemning, Michael can ask his companions among the jail representatives to make (all around stowed away) openings in a portion of the dividers (counting dividers among cells and the furthest dividers). Michael needs to have the option to escape the jail after this, regardless of which cell he is set in. Be that as it may, he likewise needs to break as couple of dividers as could be expected. Your assignment is to…Let F(x.y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Select the symbolic (s) of the following sentence: "All persons are friends with some funny and fair persons" 3x ay N(y) A R(y) →F(x,y) None of all proposed answers Vx ay N(y) A R(y) A F(x,y) Vx 3y N(x) A R(x) →F(x,y) Vx 3y N(y) A R(y) →F(x,y)TM M = (Q, E, I, 6, 90, 9a, qr), where Q = {90, 91, 92, 9a, 9r}, Σ = {0, 1}, r = {0, 1, L}, and 8 is: 8(qo, U) = (qr, U, R) 8(90, 0) = 8(go, 1) (91, 0, R) (qo, 1, R) = 8(g1, L) = (ga, U, R) 8(91,0) = (91, 0, R) 8(91, 1) = (92, 1, R) = (92, U, R) 8(92, U) 8(92, 0) = (90, 0, R) 8(92, 1) = (92, 1, R) i. Prove that M is NOT a decider. ii. Mathematically describe the language A that M recognises. Prove that A ≤ L(M). iii. Prove A = L(M). iv. Is A Turing-decidable? [Give clear reasons for your answer. No need for a formal proof.]
