By David Gries, Fred B. Schneider
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Here, the authors attempt to alter the best way common sense and discrete math are taught in machine 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 head one step extra. The publication traets common sense as a uncomplicated device that could be utilized in basically another region.
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Additional info for A Logical Approach to Discrete Math (Monographs in Computer Science)
4. Operator ~ is called consequence. Expression b ~ c is read as " b follows from c" . Operands b and c are called the consequent and antecedent, respectively. Since b => c is equal to c ~ b (according to the truth table), ~ might seem superfluous. Later, we see how it can help make some proofs more palatable. The names of operators nand and nor stand for "not and" and "not or", respectively. Expression b nand c is equal to •(b 1\ c), while b nor c is equal to •(b V c). These operators are useful when implementing switching circuits, as discussed in Sec.
TRANSLATION OF "OR" The word "or" in English is sometimes used in an inclusive sense and sometimes in an exclusive sense. The sentence "Wear a blue shirt or blue socks" would be considered inclusive, since you could wear both. e. "I'll spend my two-day vacation in Florida or I'll spend my two-day vacation in Vermont"- would be considered exclusive, since one cannot spend the two days in both places simultaneously. The inclusive sense of " b or c" is translated as b V c . 4. MODELING ENGLISH PROPOSITIONS 35 into b -=/'- c , since the exclusive or of b and c is true exactly when one of them is true and the other false .
First evaluate all the expressions Ei to yield values Vi (say); then assign v1 to x1, v2 to x2, ... , and finally Vn to Xn. Note that all expressions are evaluated before any assignments are performed. 2 are equivalent. 2. EXAMPLES OF MULTIPLE ASSIGNMENTS x,y:= x,i:= i,x:= x,i:= y,x 0,0 i+1,x+i x+i,i+1 Swap x and y Store 0 in x and i Add 1 to i and i to x Add 1 to i and i to x 1. 12) to be a list of distinct variables and E to be a list of expressions. textual substitution. 12). 3 are identical, even though the variables and expressions in the assignments appear in a different order.
A Logical Approach to Discrete Math (Monographs in Computer Science) by David Gries, Fred B. Schneider