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Translate the following English sentences into propositional logic. Your answers should be WFF s.

  1. If the Astros win the series (

    AW
    ), then pigs will fly (
    PF
    ).

  2. Pigs will not fly, and/or bacon will be free (

    BF
    ).

  3. The Astros will win the series, or bacon will be free, but not both.

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[Practice problem solution provided.]

It just so happens that all the web pages in Logiconia which contain the word

Poppins
also contain the word
Mary
. Write a formula (a query) expressing this.Use the proposition Poppins to represent the concept
the web page contains 'Poppins'
(and similar for Mary ).

Poppins Mary

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  • If a Logicanian page contains the word
    weasel
    , then it also contains either
    words
    or
    eyed
    ; and
  • Whenever a Logiconian page contains the word
    mongoose
    , it does not also contain the word
    weasel
    ; and
  • Finally, all Logiconian pages contain the word
    Logiconia
    , rather patriotically.

Write a formula expressing all this. (Your formula will involve five propositions: weasel , words , … Try to find a formula whichmirrors the wording of the English above.)

Given the above statements, if a web page in Logiconia does not contain

weasel
, does it contain
mongoose
?

Let's go meta for a moment: Is this web page Logiconian? (Yes, this one you're looking at now,the one with the homework problems.) Explain why or why not.

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Different search engines on the web have their own syntax for specifying searches.

Note that a formula may be true for some web pages, and false for others.The search engine is concerned with finding all web pages which satisfy the formula.This is called a query , in database lingo.
Only a few allow full Boolean queries. Some interpret a list of several words in a rowas an implicit conjunction, others as an implicit disjunctions.

  1. Read about the search syntax for the search language of eBay® . Write an eBay query for auctions which contain

    border
    , do not contain
    common
    , and contain at least one of
    foreign
    or
    foriegn
    [ sic , misspellings are a great way to find underexposed auctions].

  2. Google£'s advanced search is typical for the online search engines. In particular, you can search for results containing all of a , b , …, at least one of c , d , …, and none of e , f , …. Describe how that corresponds to a Boolean formula.

  3. Give an example of a Boolean formula which cannot be rewritten to conform to Google's advanced search interface.

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[Practice problem solution provided.]

A sample WaterWorld board

Consider the particular board shown in the above figure .

  1. Y-safe , Y-has-0 , and Y-has-2 are among the formulas which are true for this board but not for all boards.That is, they are neither domain axioms nor tautologies. Give two other such formulas.

  2. V-safe might or might not be true for this board.Give two other such formulas.

  1. There are many simple answers, such as Y-has-1 , W-has-1 , …

  2. There are many simple answers, such as a , N-has-1 , J-has-3 , …

For each, there are also many such formulas composed with connectives such as ∧ and ∨.

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Questions & Answers

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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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A child is a member of community not society elucidate ?
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Simon Reply
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namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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explain how nature and nurture affect the development and later the productivity of an individual.
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nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
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Source:  OpenStax, Intro to logic. OpenStax CNX. Jan 29, 2008 Download for free at http://cnx.org/content/col10154/1.20
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