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Natural Deduction Problems -
Problem 1 - Give derivations of the following:
1. ¬ (φ → ψ) → (φ Λ ¬ψ)
2. (φ → χ) ∨ (ψ → χ) from the assumption (φ Λ ψ) → χ.
Problem 2 - Prove Proposition: Γ is inconsistent iff Γ|- φ for every sentence φ.
Problem 3 - Prove that Γ|- ¬φ iff Γ U{φ} is inconsistent.
Problem 4 - Complete the proof of Theorem: (Soundness). If φ is derivable from the un-discharged assumptions Γ, then Γ |= φ.
an archaeological sample has only 25 of c-14 as much as in a living sample.knowing that the half-life of c-14 is 5800
Find the first four terms in each of two linearly independent solutions of the given differential equation (solve by means of a power series about the given point x0 ).
350 million test are expected to be sold this year. this represents 114% increase from last year. how many test were sold last year?
The Alaskan oil pipeline is 750 mi long and has a diameter of 4.0 ft.
Records indicate that t hours past midnight, the temperature at the local airport was f(t) = -0.3t^2+4t+10 degrees Celsius. what was the average temperature at the airport between 9:00am and noon?
A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.
1. Let {x1, x2, ... ,xn} be any set of n vectors in an n-dimensional vector space V. Prove that V=span{x1, x2, ... ,xn} if and only if {x1, x2, ... ,xn} is linearly independent.
What interest rate would they need to accumulate the entire $40,000 in 5 years?
a pediatric nurse is studying the number of babies born at a hospital with congenial defects.nbsp data shows that on
An air conditioning system can circulate 480 cubic feet of air per minute. How many cubic yards of air can it circulate per? minute?
In calculus and other branches of analysis, the notation (a, 8) represents the set {x Î R | a }. Consider all sets of the form (a, 8) where a Î R. What is the intersection of all of these sets?
A vortex that rotates at constant angular velocity ? about the z-axis has velocity vector field v? = ?(-yi? + xj?).
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