By David Gries, Fred B. Schneider
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Here, the authors try to alter the way in which 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 primarily some other quarter.
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Additional info for A Logical Approach to Discrete Math (Monographs in Computer Science)
1 Preliminaries A calculus is a method or process of reasoning by calculation with symbols. 1 This chapter presents a propositional calculus. It is so named because it is a method of calculating with boolean expressions that involve propositional variables (see page 33). We call our propositional calculus equational logic E. One part of E is a set of axioms, which are certain boolean expressions that define basic manipulative properties of boolean operators. e. the value of a disjunction is unchanged if its operands are swapped.
Translate the result of step 2 into a boolean expression, using "obvious" translations of the English words into operators. 3 gives examples of translations of English words. 3. TRANSLATION OF ENGLISH WORDS and, but or not it is not the case that if p then q becomes becomes becomes becomes becomes 1\ v p=>q 34 2. BOOLEAN EXPRESSIONS In programming, there is a tendency to use long identifiers to convey meaning. This is not advisable here, for long identifiers make expressions unwieldy, and symbolic manipulation then becomes painful.
Either x < y , x = y , or x > y . (b) (c) (d) (e) (f) (g) (h) (i) If x > y and y > z , then v = w . The following are all true: x < y, y < z, and v = w. At most one of the following is true: x < y, y < z, and v = w. None of the following are true: x < y, y < z, and v = w. The following are not all true at the same time: x < y , y < z , and v = w . When x < y, then y < z; when x 2: y, then v = w. When x < y, then y < z means that v = w, but if x 2: y then y > z does not hold; however, if v = w then x < y.
A Logical Approach to Discrete Math (Monographs in Computer Science) by David Gries, Fred B. Schneider