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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Concept explainers

Control structures

Control structures are block of statements that analyze the value of variables and determine the flow of execution based on those values. When a program is running, the CPU executes the code line by line. After sometime, the program reaches the point where it has to make a decision on whether it has to go to another part of the code or repeat execution of certain part of the code. These results affect the flow of the program's code and these are called control structures.

Switch Statement

The switch statement is a key feature that is used by the programmers a lot in the world of programming and coding, as well as in information technology in general. The switch statement is a selection control mechanism that allows the variable value to change the order of the individual statements in the software execution via search.

Question

f) Three distinct numbers between 10 and 25 (inclusive) are chosen at
random. What is the probability that the numbers are all composite
numbers?
g) 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?
h) 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,
d)

a) Show that (a V b → c) → (a Ab → c) is a tautology but its converse is
contingency.
b) If p → q is false, what is the truth value of ((¬p) ^ q) → (p V q)? Explain
your answer.
c) Let L(x) be the statement "x visited London", let P(x) be the statement "x
visited Paris" and let N(x) be the statement "x visited New York". Express
the 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 the
domain 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? Justify
your answer.
a) Find the number of positive integers not exceeding 120 that are divisible
by 3 or 4.
0 1 0 01
0 0
0 0 0 0. Find A[9].
0 1 0 0 0
Lo o o 1 o
го
1.
b)Let A = |1
a) How many words (with or without any meaning) can be formed by
arranging the letters in the word MEDITERRANEAN?
b) 1 red, 1 blue, 1 black, 1 yellow and 1 white car are all waiting at the traffic
lights behind each other. In how many different ways can they be waiting if
the 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. In
how many ways can a student choose 8 questions if the first three
questions are mandatory?
d) The English alphabet contains 5 vowels and 21 consonants. Find the
number of 5-letter words (with or without any meaning) composed of 3
different consonants and 2 different vowels.
e) Let A be the set of all strings of decimal digits of length 5. For example
00312 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?

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