By David Gries, Fred B. Schneider
Uploader's Note: Ripped from SpringerLink.
Here, the authors try to alter the best way common sense and discrete math are taught in desktop technological know-how and arithmetic: whereas many books deal with good judgment easily as one other subject of analysis, this one is exclusive in its willingness to move one step extra. The publication traets common sense as a easy device that could be utilized in basically another region.
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Extra info for A Logical Approach to Discrete Math (Monographs in Computer Science)
For example, suppose the state consists of (v, 5), (w, 4), (x, 8) and consider the assignment v := v +w. The value of v +w in the state is 9 , so executing v := v + w stores 9 in v , changing the state to (v,9), (w,4), (x,8). Just as important as how to execute an assignment statement is a way to reason about its effect. For example, from a precondition for an assignment, 7 how can we determine a corresponding postcondition? Or, from a postcondition, can we determine a suitable precondition? R.
Such a truth table allows us to determine the value of an expression in any state in a systematic fashion. r) t t f f f t f f t t f t f f PRECEDENCE OF BOOLEAN OPERATORS A table of precedences of operators appears on the inside front cover. Not all texts assign V and 1\ the same precedence, as we do. Sometimes, + are given the same precedence, and 1\ and · are given another, but higher, precedence. One even finds 1 used for true, 0 for false, + for V , and · for 1\ . This overloading of boolean and arithmetic operators can lead to misconceptions, because the rules for manipulation of boolean and arithmetic expressions are different.
A metatheorem is a general statement about our logic that we prove to be true. x) = x for all x. 46 3. PROPOSITIONAL CALCULUS Theorems relating =, =/= , --. r)) =r) = (p =j. (q =r)) p =j. q =r = p =q =j. 19) Mutual interchangeability: At this point, we note an interesting and useful fact about sequences of equivalences. 20) PO = P1 = ··· = Pn is true exactly when an even number of the Pi are false . Why? 3), each subexpression false Identity of by true until either one or zero false equivalents remain, in which case the sequence is false or true .