Math- Please Help!

posted by .

Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, one in a coffee shop, one in a shopping mall, and one in the library. You know the following.

a.If Kay was not discovered in the library, then Amy was discovered in the apartment building.

b.Beth was discovered in the library, unless Mary was discovered in the coffee shop.

c.If Amy was discovered in the apartment building, then Mary was discovered in the shopping mall.

d.If Beth was not discovered in the library, then neither was Kay.

If you have enough information from the statements above, match the girl with the location in which she was discovered and explain your reasoning. If you cannot make the match, explain why.
No one has answered this question yet.

  • Math- Please Help! -

    Can it even be solved?

  • Math- Please Help! -

    We can solve this problem in many ways, a truth table, or a logic tree. The latter seems more convenient, so it will be used.

    First let's use some definitions of symbols.

    For the names,
    A=Amy
    B=Beth
    K=Kay
    M=Mary

    For the locations,
    A=Apartment building
    C=Coffee Shop
    S=Shopping Mall
    L=Library

    Now the operators:
    K=L means Kay was discovered in the library (etc.)
    K≠L means Kay was not discovered in the library.
    -> means "then", or "it follows".
    and finally,
    &xor; means exclusive or, exactly one of the two statements is true.

    In logic, if the condition of a conditional statement is true, "it follows" that the following statement
    is true. If the condition is NOT satisfied, we do not know if the following statement is true or not, i.e.
    a->b
    if a is true, we know that b is true
    if a is not true, we don't know if b is true.

    "If it rains, I stay home."
    If it doesn't rain, I may stay home, or I may go out.

    Now let's get started.

    We will translate the four given statements:
    1. K≠L ->A=A
    2. B=L &xor; M=S
    3. A=A -> M=S
    4. B≠L -> K≠L

    We have two cases, either (A) K was found in the Library, or (B) she was not.

    case (A)
    K=L
    A=A (from 1.)
    B≠L (since K=L)
    But from 4, B≠L -> K≠L
    Contradiction, therefore K≠L


    Case (B)
    K≠L
    A=A (from 1, K≠L -> A=A)
    M=S (from 3 A=A -> M=S)
    B=L
    (if(B≠L, then K≠L, then nobody was found in the library; => B=L)
    K=C (by elimination)

    Conclusion:
    K=C,B=L,M=S,A=A
    If you have been following the logic, you would be able to translate the conclusion.

  • Math- Please Help! -

    Solve the following inequality. Then place the correct answer in the box provided. Answer in terms of an improper fraction.

    3y + 5 >10

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    for math im doing a survey of peoples heights and weights of like famous people and models..i was wondering how much does mary carey weigh and how tall is she?
  2. science

    Why are models useful? a) models work exactly like the things they present b) Models are the first stage in any experiment c) models are better than charts or graphs d) models are the first step in creating a prototype
  3. English

    Can you check these sentences,please? Thank you very much. 1) How big/large is the population of New York?
  4. Math

    Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, …
  5. Logic

    Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, …
  6. Math

    Lalph Rauren was famous for discovering potential models as he walked the streets of New York. One day he spotted four girls who later became top models: Amy, Mary, Kay, and Beth. One was discovered walking through an apartment building, …
  7. L/A

    Which of the following sentences contains a verb future perfect tense?
  8. MATH

    Fe walked 9/20(9 over 20) km,Beth walked twice as much as Fe,and Tina walked as much as Fe and 2/20(2 over 20) km. more.Who walked the farthest?
  9. meeting and chasing problem

    Amy and Beth live the same place which is 10 miles from the grocery store. Amy gets in her car and drives to the store at 30 miles per hour. At the same time Amy starts driving, Beth starts walking toward the store at 3 miles per hour. …
  10. statics

    A store clerk filing an order for 17 models of a new smart-phone inadvertently pulled some older models and included them in the order. There are 25 new models and 12 older models in stock when the clerk filled the order. Determine …

More Similar Questions