Results 1 to 2 of 2

Thread: Inference and Quantifiers

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    59

    Inference and Quantifiers

    Explain which rules of inference are used for each step.

    "Each of 5 roommates, Melissa, Aaron, Ralph, Veeneesha, & Keeshawn, has taken a course in discrete mathematics. Every student who has taken a course in discrete mathematics can take a course in algorithms. Therefore, all 5 roommates can take a course in algorithms next year."
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,577
    Thanks
    790
    Here is the inference in symbolic form in the case of Melissa.

    $\displaystyle \begin{array}{lll}
    1 & \mathsf{TakenDiscreteMathematics}(\mathsf{Melissa} ) & \text{Assumption}\\
    2 & \forall x\,\mathsf{TakenDiscreteMathematics}(x)\to \mathsf{CanTakeAlgorithms}(x) & \text{Assumption}\\
    3 & \mathsf{TakenDiscreteMathematics}(\mathsf{Melissa} )\to \mathsf{CanTakeAlgorithms}(\mathsf{Melissa}) & \text{From 2}\\
    4 & \mathsf{CanTakeAlgorithms}(\mathsf{Melissa}) & \text{From 3, 1}
    \end{array}
    $

    It remains for you to name the rules used in steps 3 and 4.

    In fact, assumption #1 may have been $\displaystyle \mathsf{TakenDiscreteMathematics}(\mathsf{Melissa} )\land\mathsf{TakenDiscreteMathematics}(\mathsf{Aa ron})$$\displaystyle {}\land\mathsf{TakenDiscreteMathematics}(\mathsf{R alph})\land\mathsf{TakenDiscreteMathematics}(\math sf{Veeneesha})$$\displaystyle {}\land\mathsf{TakenDiscreteMathematics}(\mathsf{K eeshawn})$. Then one has to break this first into individual conjuncts, conclude $\displaystyle \mathsf{CanTakeAlgorithms}$ for each student as shown above for Melissa, and then assemble those facts into another conjunction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inference
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: Sep 17th 2010, 10:39 AM
  2. quantifiers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Nov 6th 2009, 08:37 PM
  3. Quantifiers
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Oct 10th 2009, 08:57 PM
  4. Replies: 1
    Last Post: Aug 26th 2009, 08:04 AM
  5. Quantifiers
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Sep 2nd 2008, 10:11 AM

Search Tags


/mathhelpforum @mathhelpforum