) 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
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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)
Transcribed Image Text: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?
Transcribed Image Text: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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