1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discrete math & sentences

  1. Jan 25, 2008 #1
    Rewrite the following statement formally. Use variables and include both quantifiers [tex]\forall[/tex] and [tex]\exists[/tex] in your answer.

    Statement: Every rational number can be written as a ratio of some two integers.

    If I didn't have to use [tex]\exists[/tex] I'd write it as follows

    [tex]\forall[/tex]rational numbers x, x is a ratio of two integers.

    But I can't think of a way or any reason why I'd want to include the quantifier [tex]\exists[/tex].
  2. jcsd
  3. Jan 25, 2008 #2
    You must use variables in your answer.
  4. Jan 26, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    What does "x is a ratio of two integers" mean? That's where you need [itex]\exists[/itex].
  5. Jan 26, 2008 #4
    Ok thanks, I rewrote it as
    [tex]\forall[/tex] rational numbers x, [tex]\exists[/tex] a rational number y and a rational number z such that x=y/z.

    One more question if anyone has time to help me with.

    Rewrite the statement formally.
    Statement: There is a program that gives the correct answer to every question that is posed to it.

    So I rewrote it as
    [tex]\exists[/tex] a program p such that [tex]\forall[/tex]questions q, p always answers q correctly.
    Is this incorrectly because I have "correctly" as the final word?
    The book shows the answer as
    [tex]\exists[/tex] a program P such that [tex]\forall[/tex] questions Q posed to P, P gives the correct answer to Q.

    I didn't know if these was some technicality that would make my answer incorrect as apposed to the book's answer.
  6. Jan 26, 2008 #5
    It's mostly right except the original statement is that any rational number can be written as a ratio of 2 integers.

    For the second one, the only real problem I see is that "always" is redundant.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Discrete math & sentences
  1. Discrete math (Replies: 3)

  2. Discrete Maths (Replies: 3)

  3. Discrete Math (Replies: 2)

  4. Discrete Math Question (Replies: 9)

  5. Discrete Math Question (Replies: 9)