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- Translate the following Propositional logic into English sentences p: A student misses a lecture g: A student studies. r: A student fails. Find (a.) (q^ -p) → -r (b.) q ^ (-p → -r)6. Give the truth value of each of the following wffs in the interpretation where the domain consists of people, M(x, y) is "x is the mother of y", F(x) is "x is female", M(x) is "x is male." a. (Vx)(y)M(y,x) b. (x)(y)(M(y,x) → M(y)) 7. Which of the following sentences are equivalent to the statement Cats are smarter than dogs. a. Some cats are smarter than some dogs. b. There is a cat that is smarter than all dogs. c. All cats are smarter than all dogs. d. Only cats are smarter than dogs. e. All cats are smarter than any dog. 8. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x): x is round S(x): x is a soccer ball All soccer balls are round. a. b. Some balls are round but soccer balls are not.1. Prove or refute: (∀x, y, z, w)(B(x, y, z) ∧B(w, y, z) →B(x, w, y)).2. Prove or refute: (∀x, y, z, w)(B(x, y, z) ∧B(x, w, y) →B(w, y, z)).
- Correct answer will be upvoted else downvoted. Computer science. You are given three positive (more prominent than nothing) integers c, d and x. You need to track down the number of sets of positive integers (a,b) with the end goal that balance c⋅lcm(a,b)−d⋅gcd(a,b)=x holds. Where lcm(a,b) is the most un-normal various of an and b and gcd(a,b) is the best normal divisor of an and b. Input The primary line contains one integer t (1≤t≤104) — the number of experiments. Each experiment comprises of one line containing three integer c, d and x (1≤c,d,x≤107). Output For each experiment, print one integer — the number of sets (a,b) to such an extent that the above uniformity holds.Prove ⊢ (¬A → A) → A in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). You may not use theorem 3.31, as this is precisely that theorem.book Mordechai Ben-Ari Mathematical Logic for Computer Science Third Edition Prove {¬A} ⊢ (¬B → A) → B in Hilbert deductive system. Note: In addition to the axioms and rule of inference of H, you may use any of the derived rules and/or theorems 3.20-3.30 (as numbered in the textbook). book Mordechai Ben-Ari Mathematical Logic for Computer Science Third Edition PLEASE solve these with the help of 3 axioms and 1 rule of inference with the derived proof 3.20-3.30.Complete the logical proof for the following argument. c is an element in the domain. P(c) Vx(P(x)→ Q(x)) :. Q(c) Step AWN - Proposition c is an element in the domain P(c) → Q(c) Q(c) Justification Hypothesis
- For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was green skin, then "b" being the Hulk would make this true. Am example of this being false would be: If the domain was all integers and x was positive, even integers and "b" was integers greater than zero.The problem states that there are five philosophers sitting around a circular table. The philosophers must alternatively think and eat. Each philosopher has a bowl of food in front of them, and they require a fork in each hand to eat. However, there are only five forks available. You need to design a solution where each philosopher can eat their food without causing a deadlock.Correct answer will be upvoted else downvoted. Computer science. in case there are two planes and a molecule is shot with rot age 3 (towards the right), the cycle is as per the following: (here, D(x) alludes to a solitary molecule with rot age x) the primary plane delivers a D(2) to the left and lets D(3) progress forward to the right; the subsequent plane delivers a D(2) to the left and lets D(3) progress forward to the right; the primary plane lets D(2) forge ahead to the left and creates a D(1) to the right; the subsequent plane lets D(1) progress forward to one side (D(1) can't create any duplicates). Altogether, the last multiset S of particles is {D(3),D(2),D(2),D(1)}. (See notes for visual clarification of this experiment.) Gaurang can't adapt up to the intricacy of the present circumstance when the number of planes is excessively huge. Help Gaurang find the size of the multiset S, given n and k. Since the size of the multiset can be extremely huge, you…
- Q. Idempotency law isI. P Ú P = P.II. P Ù P = P.III. P + P = P.(a) Only (I) above(b) Only (II) above(c) Only (III) above(d) Both (I) and (II) aboveTransform the following sentences to CNF. 1. ꓯ x (P(x) ꓦ Q(x)) → R(x) 2. ꓯ x ꓯ y ꓯ z (A(x,y) ꓥ A(y,z)) → A(x,z) 3. ꓯ x ꓯ y ꓱ z P(x,z) ꓥ Q(y,z) 4. ꓯ x ⌐ [(P(x) ꓥ Q(x)) ꓦ (R(x) ꓥ S(x))]Let :P: Birds can fly.Q: 2+1=4.R: x is an integer.S: π is a rational number. CONSTRUCT THE SENTENCE OF THE FOLLOWING LOGICAL PROPOSITIONS. 1. ((p→q) ⊕ ~s) → q