Suppose P(x, y) is some binary predicate defined on a very small domain of discourse: just the integers 1, 2, 3, and 4. For each of the 16 pairs of these numbers, P(x, y) is either true or false, according to the following table (x values are rows, y values are columns). 1 2 3 4 1 T F F F T F 2 F T 3 тт тт 4 F F F F For example, P(1,3) is false, as indicated by the F in the first row, third column. Use the table to decide whether the following statements are true or false. (a) Vx3yP(x, y).

Suppose P(x, y) is some binary predicate defined on a very small domain of discourse: just the integers 1, 2, 3, and 4. For each of the 16 pairs of these numbers, P(x, y) is either true or false, according to the following table (x values are rows, y values are columns). 1 2 3 4 1 T F F F T F 2 F T 3 тт тт 4 F F F F For example, P(1,3) is false, as indicated by the F in the first row, third column. Use the table to decide whether the following statements are true or false. (a) Vx3yP(x, y).

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

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Suppose P(x,y) is some binary predicate defined on a very narrow domain ofdiscourse: just the integers 1, 2, 3, and 4. Based on the following table, P(x,y) is trueor false for each of the 16 pairs of these numbers (x values are rows, y values arecolumns).1 2 3 41 T F F F2 F T T F3 T T T T4 F F F FFor example, P(1, 3) is false, as indicated by the F in the first row, third column.Use the table to decide whether the following statements are true or false.a. ∀x∃Yp(x, y).b. ∀y∃xP(x, y).c. ∃x∀yP(x, y).d. ∃y∀xP(x, y).
Suppose P(x,y) is a predicate and the universe for the variables x and y is {1,2,3}. Suppose P(1,3),P(2.1), P(2.2), P(2.3), P(2.3), P(3.1), P(3.2) are true , and P(x,y) is false in other cases. Determinewhen the following statement is true, and specify in case there are counterexamples:a) ∀x∃yP(x,y).b) ∃x∀yP(x,y)
Consider the following predicates defined on N + .E(n) denotes “n is even”, and P (n) denotes “n is prime”. (a) Translate the following into ordinary English.i. ∃n (P (n) ∧ E(n)).ii. ∀n (E(n) ∨ ¬P (n)).iii. ¬∀n (E(n) ∨ P (n)).
Suppose L 1 is represented by 0*(0* 1*) and L 2 is represented by (0 1)*0*. Justify youranswers to the following true or false questions:a) L1 subset L 2,b) L2 subset L 1,c) L1 = L 2
Rewrite the following proposition as unambiguous English sentences. The relevant predicates are defined as follows: Again, let’s let P be a set of all people A(x) means “x is teaching the AI course” T(x) means “x is taking AI course” F(x) means “x has a twitter account.” C(x) means “x likes to read.” For example, the proposition ∃x { P [A(x)∧ C(x)]} could be translated as “There is a person who is teaching and likes to read” P [T(x) → (F(x) C(x))] ?
Given the following function, what happens if a[] contains just one element that doesn't match val? int binarySearch(int a[], int first, int last, int val){ if (first > last) return -1; int middle = (first + last) / 2; if (a[middle] == val) return middle; if (a[middle] < val) return binarySearch(a, middle+1, last, val); else return binarySearch(a, first, middle-1, val);} Group of answer choices binarySearch never calls itself again and terminates (recursion never happens) binarySearch calls itself once then terminates (recursion happens once) binarySearch calls itself twice then terminates (recursion happens twice) binarySearch calls itself 3 times then terminates (recursion happens 3 times)
Please help me Josephus Problem is a theoretical problem related to a certain counting-out game. On thiscase, people are standing in a circle waiting to be executed. After a specified number ofpeople are skipped, the next person is executed. The procedure is repeated with theremaining people, starting with the next person, going in the same direction and skippingthe same number of people, until one person remains, and is freed.Arrange the numbers 1 , 2, 3 , ... consecutively (say, clockwise) in a circle. Now removenumber 2 and proceed clockwise by removing every other number, among those thatremain, until one number is left. (a) Let denote the final number which remains. Find formula for .(b) If there are 70 people, what is the safe number (the number that remains)?
An “inverted file” is a critical data structure for implementing applications like the index of a book, or a web search engine. Given a document D (which can be viewed as an unordered, numbered list of words), an inverted file is an ordered list of words L such that for each word W in L, we store the indices of the places in D where W appears. Write a C# program (from scratch please, written by yourself (ask instructor if you are stuck), not borrowed from any other sources) that reads in a list of words separated by spaces from a text file, then uses an efficient O(N) algorithm to create the inverted file index (hint: consider the topic of this chapter, consider using a Dictionary/hashtable to help you), and writes this index out to another file or prints it to the screen. Each line of the output file should start with the next word (the words should be listed in alphabetical order, and this sorting does not have to be part of the O(N) runtime complexity, e.g. you can use regular…
A fibonacci series is defined as a series where the number at the current index, is the value of the summation of the index preceding it (index -1) and (index-2). Essentially, for a list fibonacci_numbers which is the fibonacci numbers series, fibonacci_numbers[i] = fibonacci_numbers[i-1] + fibonacci_numbers[i-2] The fibonacci series always begins with 0, and then a 1 follows. So an example for fibonacci series up to the first 7 values would be - 0, 1, 1, 2, 3, 5, 8, 13 Complete the fibonacci(n) function, which takes in an index, n, and returns the nth value in the sequence. Any negative index values should return -1. Ex: If the input is: 7 the output is: fibonacci(7) is 13 Important Note Use recursion and DO NOT use any loops. Review the Week 9 class recording to see a variation of this solution. def fibonacci(n): if (n < 0 ): return -1 else: return n fibonacci_numbers = (fibonacci[n - 1] + fibonacci[n - 2]) return fibonacci_numbers(n) # TODO: Write…
Write a C-program to read marks in the Programming and DataStructure Laboratory (out of 100) for N (to be read before) students.Consider the interval of marks 0-5, 6-10, 11-15, and so on. Note thatthe first interval contains 6 numbers, and other intervals are of 5numbers. Find the interval of marks having maximum number ofstudents in the class and compute the difference between its centerpoint from the mean of the distribution of marks.Provide results for the following inputs:1. N=2045, 56, 60, 15, 80, 90, 12, 85, 35, 58,63, 73, 52, 78, 47, 23, 14, 58, 18, 962. N=3054, 65, 6, 51, 8, 9, 21, 58, 53, 85,36, 37, 25, 87, 19, 93, 44, 85, 17, 69,40, 0, 3, 33, 16, 63, 95, 69, 74, 38
The language we are using here is in Racket. Please try tying each of the following (car '(11 12 13 14)) (car '(a b c d)) (cdr '(11 12 13 14)) (cdr '(a b c d)) (car (11 12 13 14)) (cdr (a b c d)) What do car and cdr do? That last line of the above should cause an error. Explain why the single quote necessary and what it does.
Implement the following function in C programming language that get a string, and compute an array of non-empty tokens of the string containing only lower-case letters. For example: ● For a string "abc EFaG hi", the list of tokens with only lower-case letters is ["abc", "hi"]. ● For a string "ab 12 ef hi ", the list of such tokens is ["ab","ef","hi"]. ● For a string "abc 12EFG hi ", the list of such tokens is ["ab","hi"]. ● For a string " abc ", the list of such tokens is ["abc"]. ● For a string "+*abc!! B" the list of such tokens is empty.That is, we break the string using the spaces as delimiters (ascii value 32), and look only at the tokens with lower-case letters only . The function get_tokens gets a string str, and returns the array with the tokens containing only lower-case letters in the correct order. The length of the array should be the number of tokens, computed in count_tokens. char** get_tokens(const char* str); For example:● get_tokens("abcEFaG…