10. Let p be the statement “He gets frustrated.” and q be the statement “He will be able to complete the job.” Translate ~(p ∧ q) into the equivalent statement.
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10. Let p be the statement “He gets frustrated.” and q be the statement “He will be able to complete the job.” Translate ~(p ∧ q) into the equivalent statement.
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- Let S(x) = "x is a student in our class” and P(x) = "x lives in Wahiawa" a. Assume the u.d. for x is students in our class. Translate into symbols, "There is a student in our class who lives in Wahiawa. b. Assume the u.d. for x is all people. Translate into symbols, "There is a student in our class who lives in Wahiawa.Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…
- Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…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". Vx-M(x)→ VxF(x) Vx(M(x)→ F(x)). +VæM(z) → VF(x) Vx(-M(x) → F(x))6. Given, A = p A (p V q) and B = p v (p A q). State whether A = B or not. 7. Let P(x), Q(x), and R(x) be the statements. "x is a student," “x is smart," and "x is shy," respectively. Express each of these statements using quantifiers; logical connectives; and P(x), Q(x), and R(x), where the domain consists of all people. a. Some students are shy. b. All smart people are not shy.
- Required: Amitabh had a magical cat. That cat once fell down an empty well. As the walls of the well were not completely vertical, the cat could climb up the well. In one day, the cat can climb 1 unit height and the height of the well is h units. The cat starts at the bottom. Every day, a cat would divide into 2 cats. One of them would climb up 1 unit. The other would wait for help. But while waiting it would fall asleep and roll down 1 unit, unless it is already at the bottom, in which case it just remains there. When a cat would reach the top, it would run home toAmitabh. (Schrodinger doesn't know that some of the cats are in a well and so he can't rescue them). It has been d days since the cat fell into the well. How many cats would come out of the well today? You would notice that the number of cats grows very large with each passing day, so output the answer modulo 10^9+7. d = 0 means that the cat has fallen just now and so there's just one cat at the bottom of the well. So you…3. Let K(x) be the statement “x has a pet koala,” let G(x) be the statement “x has a gazelle," let U(x) be the statement "x has a unicorn," and let F(x) be the statement "x has a farm." Express each of these statements in terms of K(x), G(x), U(x), F(x), quantifiers, and logical connectives. Let the domain consist of all people. (a) Everyone owns a gazelle or a unicorn. (b) Any person who does not own a farm cannot own a koala, gazelle, or unicorn. (c) No one owns a gazelle, but everyone owns a koala. (d) Some people own both a unicorn and a farm, but not all people own both a koala and a gazelle. (e) Each type of animal (koala, gazelle, unicorn) is owned by at least one person.Let P(X) = “x lives in Los Angeles” and the u.d. for x is all students at Cinema Club. a. Translate into symbols, “There is at least one Cinema Club student who lives in Los Angeles.” b. Using symbols, express the negation of your expression for a.
- True or False: for each of the following statements, decide if it is true or false. If it istrue, then provide a proof; if it is false, provide a counterexample.(a) For events A, B, it is always the case that Pr(Bn.A) < Pr(B).(b) For events A, B with Pr(A) > 0, it is always the case that Pr(B | A) < Pr(B).A proposition Q follows from a proposition P, if Q is never false when P is true. Suppose we want to check this in a particular case. Which of the following is correct? Select one: a. We need to check that whenever P is false, Q is also false. b. We need to check that whenever Q is false, P is also false. c. We need to check that whenever Q is true, P is also true. d. We need to check that Q is true when P is true, and that Q is false when P is false.Let D = {-1, -2, -3} and E = {−3, 1, 2, 3, 5}. Write negations for each of the following statements and determine if the given statement is true or its negation. Explain your answer. (i) V E D, ³y € E such that x + y = 0. (ii) ay € E such that vx € D, x + y ≥ 2. (iii) vy € E, 3x = D such that xy ≥ 0.