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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. $\forall x \sim P(x)$
in Mathematical Logic by Boss (10.8k points) | 51 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"

by Boss (35.4k 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.
by Boss (35.4k points)
+1 vote

.......

by Boss (35.3k 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"
by (235 points)

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