Quantified statement logic question, descrete math, wee

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In summary, the conversation discusses a college cafeteria line with four stations and the choices made by three students. The question is whether there exists a station where all students chose an item from that station. It is determined to be true, as long as each student chooses an item from the same station, but the items do not have to be the same.
  • #1
mr_coffee
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Hello everyone, i want to see if i did this correctly.

THe question refers to this:

A college cafeteria line has four stations: salads, main courses, desserts, and beverages. The salad station offers a choice of green salad or fruit salad; the main course station offers spaghetti or fish; the dessert station offers pie or cake; and the bevrage station offers milk , soda, or cofee. Three students, Uta, tim and Yuen, go through the line and make the following choices:

Uta: green salad, spaghetti, pie, milk
Tim: fruit salad, fish, pie, cake, milk, coffee
Yuen: spagehtii, fish, pie, soda

Determine wheher each of the follow statement sis true or false.

f. [tex] \exists [/tex] a station Z such that [tex]\forall[/tex] students S, [tex] \exists [/tex] an item I such that S chose I from Z.

I believe this statement says: IN a particular station Z, All students S chose a particular item I from a station.

I said True, every student S, chose pie from a particular station Z (desserts Station).

Thanks!
 
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  • #2
It's true, but not just because of that. The statement means:
There is a station such that every student chose some item from the station.
This is satisfied by the desserts station, but also by the main course station and the beverage station. If you swapped the order of "for all students S" and "Exists an item I" then it would only be satisfied by the desserts station, but as it is the items the students choose from the station do not have to be the same, so long as they each choose some item.
 
  • #3
Ahh i c now! thanks for the help! again!
:)
 

1. What is quantified statement logic?

Quantified statement logic is a branch of mathematical logic that deals with the logical relationships between statements that contain quantifiers, such as "for all" and "there exists". It is used to analyze and evaluate the truth values of complex statements.

2. How is quantified statement logic applied in discrete math?

Quantified statement logic is a fundamental tool in discrete math, as it allows for the manipulation and evaluation of mathematical statements involving quantifiers. It is used to prove theorems and solve problems in various areas of discrete math, such as combinatorics and graph theory.

3. What is the difference between discrete math and continuous math?

Discrete math deals with mathematical objects that can only take on distinct, separate values, such as integers and graphs. Continuous math, on the other hand, deals with objects that can take on any value within a given range, such as real numbers and functions.

4. Can you give an example of a quantified statement in discrete math?

An example of a quantified statement in discrete math is "For all positive integers n, there exists a positive integer m such that m = n+1". This statement uses the universal quantifier "for all" and the existential quantifier "there exists" to make a claim about the relationship between two sets of numbers.

5. What are some real-world applications of quantified statement logic?

Quantified statement logic has many real-world applications, especially in computer science and artificial intelligence. It is used in programming languages and databases to make queries and retrieve information. It is also used in automated reasoning systems and natural language processing to analyze and understand human language.

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