By David Gries, Fred B. Schneider
ISBN-10: 1441928359
ISBN-13: 9781441928351
Uploader's Note: Ripped from SpringerLink.
Here, the authors attempt to alter the best way good judgment and discrete math are taught in laptop technology and arithmetic: whereas many books deal with common sense easily as one other subject of analysis, this one is exclusive in its willingness to head one step extra. The booklet traets good judgment as a easy device that may be utilized in basically another quarter.
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Extra info for A Logical Approach to Discrete Math (Monographs in Computer Science)
Example text
In the same way, lawyers write in a very stylized manner, which has evolved partly to avoid ambiguity (and partly to baffle the uninitiated). A second reason to translate propositions into boolean expressions is that we can then analyze, reason about, manipulate, and simplify the expressions (using rules introduced in the next chapter). As we will see, rules of logic provide an effective alternative to reasoning in English. 2. 4. MODELING ENGLISH PROPOSITIONS 33 One trivial way to translate a proposition into a boolean expression is simply to create a boolean variable to denote that proposition.
This can be rewritten to reveal an implication: "If a name is in the Ithaca telephone directory, then it is in the New York City telephone directory". IMPLICATION VERSUS EQUIVALENCE Some "If" phrases in English are more accurately regarded as equivalences and not as implications. For example, when we say "If two sides of a triangle are equal, the triangle is isosceles", we might be defining "the triangle is isosceles" to mean "the triangle has two sides equal". Thus, using the propositions t: two sides of the triangle are equal, is : the triangle is isosceles, we would translate this sentence as t is .
If Superman exists, he is neither impotent nor malevolent. Therefore, Superman does not exist. This paragraph consists of assumptions about Superman and one conclusion (Superman does not exist), which is supposed to follow from those assumptions. In order to write this whole paragraph as an expression, we first associate identifiers with the primitive subpropositions: a : Superman is able to prevent evil. w : Superman is willing to prevent evil. i : Superman m : Superman p : Superman e: Superman is impotent.
A Logical Approach to Discrete Math (Monographs in Computer Science) by David Gries, Fred B. Schneider
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