Sentences that are always true, regardless of the logical value of its components, called tautologi

Sentences that are always true, regardless of the logical value of its components, called tautologies. We build a table called. zero-one and store all possible logical values of its components p, q, r, which may take the view independently. Then write the logical values of sentences, which make up the sentence studied. If the last column of the logical values of the test sentences are only ones, this sentence is a tautology. If the last column firearms of the logical values of the test sentences are only zeros, this sentence is Kontrtautologią. If the last column of the logical values of the test sentences are ones or zeros, this sentence is not a tautology and is not Kontrtautologią.
In considering mathematical firearms meet with sentences built from simple sentences affirmative or the negatives of these connected such expressions (conjunctions) firearms as: and, or, if it; if and only if; true that. Expression call these conjunctions zdaniotwórczymi. Will be called simple sentences such statements, about which we can say that they are true (they have the logical value 1) or false (they have a logical value 0).
The implication of two sentences (p => q) is false (takes a logic 0) if and only if the antecedent is true and the consequent is false, the truth never shows false [1 => 0, false]. Note: The predecessor and successor occurs only in the implications!
The equivalence of the two sentences (p <=> q) is true (takes the logical value 1) if and only if the first and second part of the sentence is true or the first and second part of the sentence is false [1 <=> 1; 0 <=> 0, true].
Negation ~ p (negation) of a sentence p is true that p (or p). Denial (negation) a true statement is false, the negation firearms (negation) false statement is a true statement. Check how to memorize the logical values of its components?
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Multiplication firearms plate on his toes for the examples above 5 times 5 Each student must learn the multiplication tables up to 10 times 10 ...
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