Define the following terms in 1-2 sentences. a) fallacy: b) essential prime implicant: c) ASCII:

a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be seen as a recursion and proof by induction is one of the easiest way to show its correctness. The structure of a proof by strong induction for one variable, say n, contains three parts. First, we define the Proposition P(n) that we want to prove for the variable n. Next, we show that the proposition holds for Base case(s), such as n = 0, 1, . . . etc. Finally, in the Inductive step, we assume that P(n) holds for any value of n strictly smaller than n' , then we prove that P(n') also holds. Use the proof by strong induction properly to show that the algorithm of the Knapsack problem above is correct.    b. Bounded Knapsack Problem: Let us consider a similar problem, in which each item i has ci > 0 copies (ci is an integer). Thus, xi is no longer a binary value, but a non-negative integer at most equal to ci , 0 ≤ xi ≤ ci . Modify the dynamic programming algorithm seen at class for this…

a) Define the following concept formally using description logics:A university has a female president, at least 5 vice presidents, all department chairs are professors whose ranks are full, and who have served the university for at least 10 years. b) Suppose we have a knowledge base-- PhD  circle-equals [AND  GraduateStudent  [FILLS :Program doctorate]]-- GraduateStudent squared-subset-or-equals Student Which of the following two sentences is a valid one? Which one can only be entailed?A) [AND Student  Male] squared-subset-or-equals StudentB) [AND PhD Male] squared-subset-or-equals Student

2) Answer the following questions (Unit 2):  a. What is a compound sentence? b.What is a sentential operator?

Can you please help me with this problem because I don't understand how to do this problem. Can you please help me with this problem. Can you please explain this step by step.

Need the right answer among choices and also an explanation of the answer.

Question 11 Please choose the perfect answer only.

1): Select the law which shows that the two propositions are logically equivalent. ¬((w∨p)∧(¬q∧¬w)) ¬(w∨p)∨¬(¬q∧¬w) A): DeMorgan’s law B): Distributive law C): Associative law D): Complement law     2):  Select the proposition that is a tautology.  (p∧q)→¬p  (p∨q)→p  (p∧q)↔p     4 . (p∧q)→p   A): 4 B): 1 C): 2 D): 3

Proofs: Construct proofs to show that the following symbolic arguments are valid. Commas mark the breaks between premises, ‘∴’ precedes the conclusion. You may use the following rules: MP, MT, DS, HS, CD, Simp, Conj, Add ∼N • ∼M, ∼P → N, ∼N → Z, (Z • ∼∼P) → K ∴ K • ∼M

Part 1: Choose two of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the arguments. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. 1.(G • P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G • ~L) → K 2.(S v T) ↔ ~E, S → (F • ~G), A → W, T → ~W, therefore, (~E • A) → ~G 3.(S v T) v (U v W), therefore, (U v T) v (S v W) 4.~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B 5.~S → (F → L), F → (L → P), therefore, ~S → (F → P) Part 2: Below are basic arguments in English. Choose two arguments and translate those argument into the symbolism of predicate logic. You do not need to do a proof. Every fetus has an immortal soul. A thing has an immortal soul only if it has a right to life. Hence, every fetus has a right to life. (Fx = x is a fetus, Sx = x has an immortal soul, Rx = x has a right to life). Some wars are just. No war of…