Search & Filtering
Let C(x) be the statement “x has a cat,” let D(x) be the statement “x has a dog,” and let F(x) be the statement “x has a ferret.” Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.
Translate these statements into English, where C(x) is “x is a comedian” and F(x) is “x is funny” and the domain consists of all people. a) ∀x(C(x) → F(x)) b) ∀x(C(x) ∧ F(x)) c) ∃x(C(x) → F(x)) d) ∃x(C(x) ∧ F(x))
Let P(x) be the statement “x spends more than five hours every weekday in class,” where the domain for x consists of all students. Express each of these quantifications in English.
a) ∃xP(x) b) ∀xP(x) c) ∃x ¬P(x) d) ∀x ¬P(x)
Determine whether each of these sets is the power set of a set. where a and b are distinct elements.
a) ∅
b) {∅.{∅}}
c) {∅, {a}. {∅, a)}
d) {∅, {a}. {b}. {a, b}}
Calculate the width of the class with boundaries 5 and 30.
Prove that the union of a finite number of open sets is open
Test the series ∞ Σ n=1 (-1)^n-1. 3/(5n-2) for absolute and conditional convergence
The function f(x)= [x]- x is not integrable in [ 0,3] , where [ x] denote greatest integer function.
True or false with full explanation
Let A and B be two non-empty sets. Show that A × B = B × A if and only if A = B.
The probability that an American industry will locate in Shanghai China is 0.70, in Beijing is 0.40 and in either Shanghai or Beijing or both is 0.80. what is the probability that the industry will locate : a) in both cities, b) in neither city
