f) Three distinct numbers between 10 and 25 (inclusive) are chosen atrandom. What is the probability that the numbers are all compositenumbers?g) Suppose that you pick a bit string from the set of all bit strings of lengthten. What is the probability that the bit string has more Os than 1s?h) Suppose we want to pick two numbers from {1,2, .,100} randomly. Whatis the probability that the sum of the two picked numbers is divisible by 5,d) a) Show that (a V b → c) → (a Ab → c) is a tautology but its converse iscontingency.b) If p → q is false, what is the truth value of ((¬p) ^ q) → (p V q)? Explainyour answer.c) Let L(x) be the statement "x visited London", let P(x) be the statement "xvisited Paris" and let N(x) be the statement "x visited New York". Expressthe statement "None of your friends visited London, Paris and New York."in terms of C(x), D(x), F(x), quantifiers, and logical connectives where thedomain consists of all your friends.a) Let A, B, U and V be any sets such that A C U and B C V. Is (A × B) C(U X V)? Justify your answer.b) Suppose f: R → Z where f(x) =[2x – 11.i. If A = {x |1 < x < 4}, find f (A).ii. If B = {3,4,5,6,7}, find f (B).iii. If C = {-9, –8}, find f-1(C).c) Let f:R → R be defined by f (x) = 2x2 + 2x – 12. Is fone-to-one? Justifyyour answer.a) Find the number of positive integers not exceeding 120 that are divisibleby 3 or 4.0 1 0 010 00 0 0 0. Find A[9].0 1 0 0 0Lo o o 1 oго1.b)Let A = |1a) How many words (with or without any meaning) can be formed byarranging the letters in the word MEDITERRANEAN?b) 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the trafficlights behind each other. In how many different ways can they be waiting ifthe black car and only the black car is between the white and yellow cars?c) Students need to answer 8 out of 10 questions in mathematics exam. Inhow many ways can a student choose 8 questions if the first threequestions are mandatory?d) The English alphabet contains 5 vowels and 21 consonants. Find thenumber of 5-letter words (with or without any meaning) composed of 3different consonants and 2 different vowels.e) Let A be the set of all strings of decimal digits of length 5. For example00312 and 19483 are two strings in A. You pick a string from A at random.What is the probability that the string has no 4 in it?

Answer is given below . Note : You have asked so many questions as per policy i can not answer them…

) Three distinct numbers between 10 and 25 (inclusive) are chosen at random. What is the probability that the numbers are all composite numbers? :) Suppose that you pick a bit string from the set of all bit strings of length ten. What is the probability that the bit string has more Os than 1s? 1) Suppose we want to pick two numbers from {1,2, .,100} randomly. What is the probability that the sum of the two picked numbers is divisible by 5,

) Three distinct numbers between 10 and 25 (inclusive) are chosen at random. What is the probability that the numbers are all composite numbers? :) Suppose that you pick a bit string from the set of all bit strings of length ten. What is the probability that the bit string has more Os than 1s? 1) Suppose we want to pick two numbers from {1,2, .,100} randomly. What is the probability that the sum of the two picked numbers is divisible by 5,

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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Show the following:(a) p ∧ t ≡ p, where t is a tautology.(b) p ∧ c ≡ c, where c is a contradiction.(c) ∼ t ≡ c and ∼ c ≡ t, where t is a tautology and c is a contradcition. (d) p ∨ p ≡ p and p ∧ p ≡ p.
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