Proofs are best done with your Boolean goggles on, so I suggest first writing #4 and #7 in Boolean form. For the first four questions, show that the argument is TT con by providing a formal proof. [Hint: The first two are really easy, needing only Elim, ^Intro and Intro. Don't overthink them!] 1. | (Av B) ^¬(C^¬D) CA(AB) |(Av B) ^¬(A ^ B) 2. | (-AVC) ^ B C (AV B) AC 3. ||-(A v B) B 4. |-Cube(c) |—Tet(c) ― (Tet(c) v Cube(c))
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- Can you please help me with this problem because i am having a difficult time trying to figure out how to do this problem that I don't understand. Can you please do it step by step and can you explain it in full detail expllaining leading up to the answer.Computer science. Correct answer will be upvoted else downvoted. You have an at first void cauldron, and you need to blend an elixir in it. The elixir comprises of two fixings: enchantment pith and water. The elixir you need to blend ought to contain precisely k % sorcery substance and (100−k) % water. In one stage, you can pour possibly one liter of sorcery pith or one liter of water into the cauldron. What is the base number of steps to mix a mixture? You couldn't care less with regards to the complete volume of the elixir, just with regards to the proportion between sorcery substance and water in it. A little update: in the event that you pour e liters of embodiment and w liters of water (e+w>0) into the cauldron, then, at that point, it contains ee+w⋅100 % (without adjusting) sorcery substance and we+w⋅100 % water. Input The primary line contains the single t (1≤t≤100) — the number of experiments. The sole line of each experiment contains a solitary integer k…Correct answer will be upvoted else downvoted. Computer science. Positive integer x is called divisor of positive integer y, in case y is distinguishable by x without remaining portion. For instance, 1 is a divisor of 7 and 3 isn't divisor of 8. We gave you an integer d and requested that you track down the littlest positive integer a, to such an extent that a has no less than 4 divisors; contrast between any two divisors of an is essentially d. Input The primary line contains a solitary integer t (1≤t≤3000) — the number of experiments. The primary line of each experiment contains a solitary integer d (1≤d≤10000). Output For each experiment print one integer a — the response for this experiment.
- Module 6 Journal. Please complete each of the proofs below. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8. (D→C) • (C→ D), E → -(D → C) :. -E F • (G V H), -F V -H : F. G -U → ~B, S → ~B, ~(U • -S), TV B .:. T 3. (QR) V (-Q • -R), N → ~(Q ↔ R), EV N.. E -X → -Y, -Xv -Y, Z →Y: -Z -M V N, -R→-N : M → RPython answer only. Correct answer will upvoted else downvoted. It is the ideal opportunity for your very first race in the game against Ronnie. To make the race intriguing, you have wagered a dollars and Ronnie has wagered b dollars. Yet, the fans appear to be frustrated. The fervor of the fans is given by gcd(a,b), where gcd(x,y) means the best normal divisor (GCD) of integers x and y. To make the race seriously invigorating, you can perform two kinds of activities: Increment both an and b by 1. Diminishing both an and b by 1. This activity must be performed if both an and b are more noteworthy than 0. In one action, you can play out any of these activities. You can perform self-assertive (potentially zero) number of moves. Decide the greatest energy the fans can get and the base number of moves needed to accomplish it. Note that gcd(x,0)=x for any x≥0. Input The principal line of input contains a solitary integer t (1≤t≤5⋅103) — the number of experiments.…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…
- Stuck need help! The class I'm taking is computer science discrete structures. Problem is attached. please view attachment before answering. Really struggling with this concept. Thank you so much.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…Correct answer will be upvoted else downvoted. Computer science. string a matches an example b if for every I from 1 to k either bi is a special case character or bi=ai. You are approached to improve the examples so that the primary example the j-th string matches is p[mtj]. You are permitted to leave the request for the examples unaltered. Would you be able to perform such an improvement? Assuming you can, print any legitimate request. Input The primary line contains three integers n, m and k (1≤n,m≤105, 1≤k≤4) — the number of examples, the number of strings and the length of each example and string. Every one of the following n lines contains an example — k characters that are either lowercase Latin letters or highlights. All examples are pairwise unmistakable. Every one of the following m lines contains a string — k lowercase Latin letters, and an integer mt (1≤mt≤n) — the record of the main example the relating string should coordinate. Output Print "NO"…
- Can you help me with this problem because I am struggling and i don't know what to do. I only need help with part A and C. Can you please show all your work so I can understand how you did it and can you explain it in full detail step by step. Again I only need help with part A and Part C. Thank you.What’s the language of the regular expression b, i.e., the set of all strings that can be recognized by the regular expression? 1) {a} 2) {b} 3) b 4) {b, bb, bbb, ...} I selected 3 and was told it was wrong. I thought that regular expression b could only be recognized by the string(s) b. Without a closure operator (*) there is no repeating so I assumed it couldnt be 4, and since theirs no {} it couldnt be 2. Can someone explain please.Conway's Game of Life: This is a zero person game with the following rules: (see Wikipedia for example) Any live cell with fewer than two live neighbours dies, as if by underpopulation. Any live cell with two or three live neighbours lives on to the next generation. Any live cell with more than three live neighbours dies, as if by overpopulation. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction. Remember the oscillator or blinker of 3 cells. You can also find this blinker on Wikipedia. 1 21 1 2 1 21 3. 4 6 4. 6. 4 8. 9 8 9 #1 #2. #3 5. Consider now these 3 creatures at stage 1: Show how they look like in the next two stages: stage 2 and stage 3. Explain how you get the answers Creature 1 Creature 2 Creature 3 (here creature 1 is the blinker of 3 cells, horizontally; creature 2 consists of two adjacent cells, creature 3 consists of 4 adjacent cells horiztonally) ww (d) Creature 1 (10%), (e) Creature 2 (8%), (f) Creature 3 (20%)