Download PDF by David Gries, Fred B. Schneider: A Logical Approach to Discrete Math (Monographs in Computer

By David Gries, Fred B. Schneider

ISBN-10: 1441928359

ISBN-13: 9781441928351

Uploader's Note: Ripped from SpringerLink.

Here, the authors try to alter the way in which good judgment and discrete math are taught in desktop technology and arithmetic: whereas many books deal with common sense easily as one other subject of research, this one is exclusive in its willingness to move one step extra. The publication traets good judgment as a uncomplicated device that may be utilized in basically any other region.

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Extra resources for A Logical Approach to Discrete Math (Monographs in Computer Science)

Sample text

And finally = and =/=. In view of the importance of Leibniz and equivalence in our calculus, we choose the order = (and = ), --, and =/= (and =I), V, 1\, and finally =? and {::::. 2 All theorems of our propositional calculus are valid (see Def. 1) on page 31). This fact can be established by (i) checking each axiom with a truth table and (ii) arguing for each inference rule that if its premises are valid then so is its conclusion. Not only are all theorems valid, but all valid expressions are theorems of our calculus (although we do not prove this fact).

I 1\ •m 6 This example, taken from [2], is adapted from an argument about the nonexistence of God in [17]. 38 2. BOOLEAN EXPRESSIONS The paragraph about Superman asserts that its last sentence follows from the first four, so it can be written as the following expression: FO 1\ Fl 1\ F2 1\ F3 => •e . e. a boolean variable) to each sentence now becomes clear; had we used the sentences themselves instead of their names, the final expression would have been long and unwieldy. To determine the validity of the Superman paragraph, we have to see whether this expression is true in all states.

Ei mz: E[r := P] = E[r := Q] • • • P=Q, Q=R Transitlvity: p = R Substitution: P[r 1 ~= Q] From Webster's Third New International Dictionary. D. , A Logical Approach to Discrete Math © Springer Science+Business Media New York 1993 42 3. PROPOSITIONAL CALCULUS A theorem of our propositional calculus is either (i) an axiom, (ii) the conclusion of an inference rule whose premises are theorems, or (iii) a boolean expression that, using the inference rules, is proved equal to an axiom or a previously proved theorem.

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A Logical Approach to Discrete Math (Monographs in Computer Science) by David Gries, Fred B. Schneider

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