Wikipedia
compound proposition : Logic, from the Greek λογική (logiké) is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its fundamental place in philosophy. It became part of the classical trivium, a fundamental part of a classical education, and is now an integral part of disciplines such as mathematics, computer science, and linguistics. Logic concerns the structure of statements and arguments, in formal systems of inference and natural language. Topics include validity, fallacies and paradoxes, reasoning using probability and arguments involving causality and time. Logic is also commonly used today in argumentation theory. The concept of logical form is central to logic; it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic lo.... More from Wikipedia
compound proposition : In integrated circuit design, dynamic logic (or sometimes clocked logic) is a design methodology logic family in digital logic that was popular in the 1970s and has seen a recent resurgence in the design of high speed digital electronics, particularly computer CPUs. Dynamic logic is distinguished.. More from Wikipedia
Logical connectives and compound statements
Normally propositions are joined by 'OR', 'AND', 'NOT', 'IF .. THEN..' and 'IF AND ONLY IF' called the logical connectives . They are symbolised as follows: If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting statement is ..
Normally propositions are joined by 'OR', 'AND', 'NOT', 'IF .. THEN..' and 'IF AND ONLY IF' called the logical connectives . They are symbolised as follows: If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting statement is ..Note:
Suppose a compound proposition is given, we first split it into simple propositions containing a single connective. Using the rules discussed above, we construct the truth table in the form of columns and the last column gives the truth value of the given proposi..
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Question : Find a compound proposition involving the propositional variables p, q and r that is true when exactly two of p, q and r are true and is false otherwise.
How would I solve this question? It would be better if you could make me understand the easy way.
Your reply is much appreciated.
Answer : There's a systematic way to generate propositions from a truth table. In each row, you are given a particular combination of T/F values of the propositions, for which you get a T/F value of the compound proposition. So when is your statement true? (p and q and not r) or (p and not q and r) or (not p and q and r). Basically use disjunctions between the rows of the truth table. You can then reduce this expression to something more compact (probably throw in xor)... More from Yahoo Answers
Answer : There's a systematic way to generate propositions from a truth table. In each row, you are given a particular combination of T/F values of the propositions, for which you get a T/F value of the compound proposition. So when is your statement true? (p and q and not r) or (p and not q and r) or (not p and q and r). Basically use disjunctions between the rows of the truth table. You can then reduce this expression to something more compact (probably throw in xor)... More from Yahoo Answers
Question :
Answer : p q p implies q ~p ~pvq p implies q if and oonly if ~pvq T T T F T T T F F F F T F T T T T T F F T T T T.. More from Yahoo Answers
Answer : p q p implies q ~p ~pvq p implies q if and oonly if ~pvq T T T F T T T F F F F T F T T T T T F F T T T T.. More from Yahoo Answers
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