Disc Math Logic statements (Homework check)

In summary, the conversation was about three logical statements involving quantifiers and implications. The first statement states that for every faculty member, there is a student who has not asked a question of that faculty member. The second statement states that there exists a faculty member for whom every student has not asked a question. The third statement states that there exists a faculty member and a student who, when the student asks the faculty member a question, the faculty member answers it. The conclusion is that the first two statements are not equivalent, but the third statement appears to be correct.
  • #1
Miike012
1,009
0
My solution
d. [itex]\forallx[/itex][itex]\existsy[/itex](F(x)^S(y) → [itex]\negA(y,x)[/itex])
e. [itex]\existsx[/itex][itex]\forally[/itex](F(x)^S(y) → [itex]\negA(y,x)[/itex])
f.[itex]\existsx[/itex][itex]\forally[/itex](S(x)^F(y) → A(x,y))
 

Attachments

  • LL.jpg
    LL.jpg
    19.3 KB · Views: 469
Physics news on Phys.org
  • #2
Miike012 said:
My solution
d. [itex]\forall x[/itex] [itex]\exists y[/itex](F(x)^S(y) → [itex]\neg A(y,x)[/itex])
e. [itex]\exists x[/itex] [itex]\forall y[/itex](F(x)^S(y) → [itex]\neg A(y,x)[/itex])
f.[itex]\exists x[/itex] [itex]\forall y[/itex](S(x)^F(y) → A(x,y))

For d: You have "for every faculty member, there is a student who has not asked a question of that faculty member". That's not equivalent to "some student has not asked a question of any faculty member", because in the first it might not be the same student in each case. You need to swap the quantifiers.

The others appear to be correct.
 

What is Disc Math Logic?

Disc Math Logic is a mathematical system that uses discs and arrows to represent logical statements. It is used to solve problems and make arguments based on logical reasoning.

What are the basic components of Disc Math Logic statements?

The basic components of Disc Math Logic statements are discs, arrows, and logical operators. Discs represent statements, arrows represent relationships between statements, and logical operators (such as "and", "or", "not") are used to connect and modify the statements.

How do you solve a Disc Math Logic problem?

To solve a Disc Math Logic problem, you need to carefully analyze the given statements and use logical reasoning to determine the relationship between them. Then, you can use the given logical operators to connect and modify the statements to reach a conclusion.

What are the common mistakes when using Disc Math Logic?

One common mistake when using Disc Math Logic is misinterpreting the arrows. It's important to carefully consider the direction and meaning of each arrow in the statement. Another mistake is not using the correct logical operators to connect the statements, which can lead to incorrect conclusions.

How can practicing Disc Math Logic improve critical thinking skills?

Practicing Disc Math Logic can improve critical thinking skills by training individuals to analyze and evaluate information in a logical and systematic way. It also helps to strengthen deductive and inductive reasoning skills, which are essential in problem-solving and decision-making.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
820
  • Precalculus Mathematics Homework Help
Replies
5
Views
917
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
721
  • Calculus and Beyond Homework Help
Replies
5
Views
536
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
614
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
453
Back
Top