Question on Predicate Logic "If Then" and "x if y" Here is the question I have: “There exists a res

veneciasp 2022-07-08 Answered
Question on Predicate Logic "If Then" and "x if y"
Here is the question I have: “There exists a restaurant that, if it is midnight, then this restaurant would not be open.” and “Not all restaurant are open if it is midnight.” Assume the set of all restaurant as the universe of discourse.
I assume P(x) is the case that the restaurant will not be open and A is the event that it is midnight.
And I got x ( A P ( x ) ) for both sentences. Is there anything I did wrong? Since the question assumes there will be two individual answers for the statements, and have a sub-question requiring me to prove these two logic notation to be logically equivalent.
You can still ask an expert for help

Want to know more about Discrete math?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Nirdaciw3
Answered 2022-07-09 Author has 20 answers
Step 1
And i got " x ( A P ( x ) ) " for both sentence, Is there anything i did wrong?
The first statement reads: “There exists a restaurant that, if it is midnight, then that restaurant would not open” which is indeed x   ( A P ( x ) ).
Step 2
The second statement reads: “Not all restaurant open if it is midnight” which is also "If it is midnight, then not all restaurants open," which is slightly different. The immediate translation is: A ( ¬ x   ¬ P ( x ) )
Those are the distinct answers you were expected to obtain first, and then you may show equivalence by applying rules of equivalence.
Did you like this example?
Subscribe for all access
kramberol
Answered 2022-07-10 Author has 5 answers
Step 1
You are correct.
The second sentence literally says
A ¬ x ¬ P ( x ) ,,
which is logically equivalent to
A x P ( x ) ,
Step 2
which is logically equivalent to
x ( A P ( x ) ) ,,
which is literally what the first sentence says.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-08-15
How many elements are in the set { 0, { { 0 } }?
asked 2021-08-18

Discrete Mathematics Basics

1) Find out if the relation R is transitive, symmetric, antisymmetric, or reflexive on the set of all web pages.where (a,b)R if and only if 
I)Web page a has been accessed by everyone who has also accessed Web page b.
II) Both Web page a and Web page b lack any shared links.
III) Web pages a and b both have at least one shared link.

asked 2021-07-28

Let A, B, and C be sets. Show that (AB)C=(AC)(BC)
image

asked 2020-11-09
Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.
asked 2021-11-07
Use symbols to write the logical form of the following arguments. If valid, iden— tify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error has been made. If you study hard for your discrete math final you will get an A. Jane got an A on her discrete math final. Therefore, .lane must have studied hard.
asked 2022-06-23
Proof by contradictions
Theorem: For all a, b, c in Z Z if a does not divide b c, then a does not divide b or a does not divide c. Prove by contradiction
I know the first step is to flip the theorem to "there exists a,b,c in Z such that a does not divide b c and a divides b and a divides c" but I am lost as to how to continue the proof.
asked 2021-07-30
Solve the following recurrence relation:
a) an+1=dan+c, a0=0
b) an+13=2an3, a0=5
c) Fn=5Fn16Fn2, F0=1 and F1=4

New questions

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question