The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+1 vote
47 views

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 qualifications in English.

  1. $\exists x P(x)$
  2. $\forall x P(x)$
  3. $\exists x \sim p(x)$
  4. $\forall x \sim P(x)$
asked in Mathematical Logic by Boss (10.8k points) | 47 views

4 Answers

+1 vote

P(x) is “spends more than five hours every weekday in class”

a) xP(x) "There exist a student who spends more than five hours every weekday in class"

b) xP(x) "All students spend more than five hours evert weekday in class"

c) ¬P(x) "There exist a student who does not spend more than five hours every weekday in class"

d) ¬P(x) "Every Student don't spend more than 5 hours every weekday in class"

answered by Boss (34.6k points)
0
I think option D can be written like this
d) "There is no student who spends more than five hours every weekday in class."
0

that would be ¬∃xP(x) which is correct when we apply de morgan's law 

+1 vote
1. $\exists x P(x)$

There exists a student who spends more than five hours every weekday in class.

2. $\forall x P(x)$

All students spends more than five hours every weekday in class.

3. $\exists x \sim P(x)$

There exists a student who do not spend more than five hours every weekday in class.

4. $\forall x \sim P(x)$

All students do not spend more than five hours every weekday in class.
answered by Boss (34.6k points)
+1 vote

.......

answered by Boss (34.2k points)
0 votes
a.∃xP(x)

There is a student who spends more than five hours every weekday in class.

b.∀xP(x)

All student spends more than five hours every weekday in class.

 

c.∃x∼P(x)

There is a student who does not spend more than five hours every weekday in class.

 

d.∀x∼P(x)

All students do not spend more than five hours every weekday in class.

Another way to write the same statement as "No student spends more than five hours every weekday in class"
answered by (235 points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
49,814 questions
54,521 answers
188,389 comments
75,429 users