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43 Pages
logic_definitions
Course: MATH 245, Spring 2008School: JMU
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Word Count: 704
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in Counting Binary 000 001 010 011 100 101 110 111 etc. (Lots of) Denitions (Lots of) Denitions Proposition (Lots of) Denitions Proposition A proposition is a declarative sentence that is either true or false. Denition Denition Negation Denition Negation Let p be a proposition. The statement It is not the case that p. is another proposition called the negation of p. Notation: p. Denition Denition...
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in Counting Binary
000 001 010 011 100 101 110 111 etc.
(Lots of) Denitions
(Lots of) Denitions
Proposition
(Lots of) Denitions
Proposition
A proposition is a declarative sentence that is either true or false.
Denition
Denition
Negation
Denition
Negation
Let p be a proposition. The statement It is not the case that p. is another proposition called the negation of p. Notation: p.
Denition
Denition
Conjunction
Denition
Conjunction
Let p and q be propositions. The conjunction of p and q, denoted p q, is the proposition that is true when both p and q are true, and is false otherwise. (Less formally, this is also known as p and q.)
Denition
Denition
Disjunction
Denition
Disjunction
Let p and q be propositions. The disjunction of p and q, denoted p q, is the proposition that is false when both p and q are false, and is true otherwise. (Less formally, this is also known as p or q.)
Denition
Denition
Exclusive or
Denition
Exclusive or
Let p and q be propositions. The exclusive or of p and q, denoted p q, is the proposition that is true when exactly one of p and q is true, and is false otherwise.
Denition
Denition
Implication
Denition
Implication
Let p and q be propositions. The implication p q is the proposition that is false when p is true and q is false, and is true otherwise.
Denition
Implication
Let p and q be propositions. The implication p q is the proposition that is false when p is true and q is false, and is true otherwise. In the implication p q, statement p is called the hypothesis, antecedent or premise.
Denition
Implication
Let p and q be propositions. The implication p q is the proposition that is false when p is true and q is false, and is true otherwise. In the implication p q, statement p is called the hypothesis, antecedent or premise. The statement q is called the conclusion or consequence.
Denition
Denition
Converse
Denition
Converse
The implication q p is the converse the of implication p q.
Denition
Denition
Inverse
Denition
Inverse
The implication p q is the inverse of the implication p q.
Denition
Denition
Contrapositive
Denition
Contrapositive
The implication q p is the contrapositive of the implication p q.
Denition
Denition
Biconditional
Denition
Biconditional
Let p and q be propositions. The biconditional p q is the proposition that is true when p and q have the same truth values, and is false otherwise. (Often stated as p if, and only if, q, or more briey p i q.)
Denitions
Denitions
Tautology
Denitions
Tautology
A tautology is a compound statement that is always true, no matter the truth values of the individual statements.
Denitions
Tautology
A tautology is a compound statement that is always true, no matter the truth values of the individual statements.
Contradiction
Denitions
Tautology
A tautology is a compound statement that is always true, no matter the truth values of the individual statements.
Contradiction
A contradiction is a compound statement that is always false, no matter the truth values of the individual statements.
Denitions
Tautology
A tautology is a compound...
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