Problem 03: (a) Use a truth table to determine whether the statements (pv-q) ^ (pv q) and ~p V (p ^ q) are logically equivalent or not. Copy down the following tables on your answer sheet and fill them out. ● Truth table for (pv~q) ^ (pv q) р q Р Truth table for p V (p ^ q) ~q q PV~q P^ q I pvq ~P (pv~q) ^ (pv q) ~pv (p ^ q)

Problem 03: (a) Use a truth table to determine whether the statements (pv-q) ^ (pv q) and ~p V (p ^ q) are logically equivalent or not. Copy down the following tables on your answer sheet and fill them out. ● Truth table for (pv~q) ^ (pv q) р q Р Truth table for p V (p ^ q) ~q q PV~q P^ q I pvq ~P (pv~q) ^ (pv q) ~pv (p ^ q)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!
Determine whether ∀x(P (x) ↔ Q(x)) and ∀x P (x) ↔∀xQ(x) are logically equivalent. Justify your answer
I don't need a code for these questions. I just need them answered Nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The results are presented in the following table:Temperature (OC)Corrosion(mm/yr.)26.6 1.5826 1.4527.4 1.1321.7 0.9614.9 0.9911.3 1.0515 0.828.7 0.688.2 0.59a. Construct a scatterplot of corrosion (y) vs. temperature (x). Verify that a linear model is appropriate.b. What is the least-square line (trendline/regression line) for predicting corrosion from temperature?c. Two steel specimens whose temperatures differ by 10OC are submerged in seawater. By how much would you predict their corrosion rates differ?d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20OC.e. Construct a table with predicted values from the original dataset.f. Compute the residuals. Which point has the residual with the largest magnitude?g. What is the correlation between temperature and corrosion rate? What…
2) (L2) Prove using laws of logic that the conditional proposition (p ∧ q) → r is equivalent to (p ∧ ¬ r) →¬ q. 3) (L3) Show that the converse of a conditional proposition p: q → r is equivalent to the inverse of proposition p using a truth table. 4.1) (L4) Show whether ((p ∧ (p→q)) ↔ ¬p) is a tautology or not. Use a truth table and be specific about which row(s)/column(s) of the truth table justify your answer. 4.2) (L4) Give truth values for the propositional variables that cause the two expressions to have different truth values. For example, given p ∨ q and p ⊕ q, the correct answer would be p = q = T, because when p and q are both true, p ∨ q is true but p ⊕ q is false. Note that there may be more than one correct answer. r ∧ (p ∨ q) (r ∧ p) ∨ q
Q#7. Construct a truth table for each of these compound propositions. a) (p→q)∧(¬p→q) b) (p↔q)∨(¬p↔q)
For Hamming’s rule, d = 4 and m = 3 is a “perfect” solution to 2m = m + d + 1. For the next smaller perfect solution; that is, m<3, d<4, what is m? , what is d? Construct or imagine constructing the Hamming code (the table) for this new perfect solution. Using the same format as the table in the previous question, and leaving out the top 2 rows, how many rows in the table? How many columns? Leave out the column with D and the ? mark. What is another name for this code? (Besides Hamming (3,1) What is the hamming distance of this code?
CONSTRUCT THE TRUTH TABLE OF THE FOLLOWING PROPOSITIONS. 1. p→ (p ν q)
2. Construct a truth table for each of these compound propositions.a) [¬p∧(p∨q)]→qb) [(p→q)∧(q→r)]→(p→r)c) [p∧(p→q)]→qd) [(p∨q)∧(p→r)∧(q→r)]→r
3. Display the following on a common, four-case truth table. Use “M” and “C” for “Moriarty is guilty” and “Crun is guilty.” (a) Either Moriarty and Crun are both guilty or Crun is innocent. (b) Either Crun is guilty or both he and Moriarty are. (c) Either Moriarty is guilty or both he and Crun are innocent. (d) Either Moriarty is guilty or Crun is innocent or both are guilty. (e) They are not both guilty, and at least one is innocent. j i f) Either both are guilty or Moriarty is but Crun is not. (g] Either they are not both guilty or they are not both innocent. Which are tautologies? Among the rest, which imply which others? Which imply that Moriarty is guilty? Which imply that Crun is guilty? The seven statements a to g are not jointly satisfiable, but certain six membered subsets are. Which? Which of the seven are individually satisfiable?
Use indirect truth tables to determine whether the following arguments are valid or invalid. a) ~A ⊃ ~(~B • C)D ⊃ ~BE ⊃ ~(F • ~G)E v D--------------------F • A b) (Z v W) ⊃ (X v Y)X ⊃ (Y • U)(U v V) ⊃ T--------------------Z ⊃ G c) A ⊃ (F v G)F ⊃ (D v S)G ⊃ (M v D)(M v S ) ⊃ D--------------------A ⊃ D
1]To check if ¬(p∨q)¬(p∨q) and ¬p∧¬q¬p∧¬q are logically equivalent? 2] A truth table for (p∧q)→¬(p∨q)(p∧q)→¬(p∨q).