2.13.12 ISSUE 8: Math Quiz//Logic
Made By: Miyu Em {@}>;--
Logic is the study of reasoning
Mathematical Sentence: A sentence is a sentence that contains a complete thought and can be judged to be true and false
Phrase: An expression that is part of a sentence
Open Sentence: Any sentence that contains a variable
Domain/ Replacement Set: Set of numbers that can replace a variable
Solution Set/ True Set: Set of all replacement that will change an open sentence or true sentence
Statement/ Close Sentence: A sentence that can be judged to be true or false
Truth Value: A close sentence has this. Either True or False
Negation: Statement with an opposite truth value of an given statement
Compound Sentence: A combination of two or more mathematical sentences formed by using the connectives not, and, or, if...then, or if and only if.
Conjunction: A compound statement formed by combining two simple statements, called conjuncts, with the word AND. The conjunction is usually formed by using the symbols
p ^ q.
Disjunction: A compound statement formed by combining two simple statements, called disjuncts, with the word OR. The disjunction is usually formed by using the symbols p v q.
Truth Table: A summary of all possible truth values of a logic statement.
Conditional: A compound statement formed by using the words if...then to combine two simple statements. The conditional if p then q is writing symbolically as p --> q.
Hypothesis/Premise/ Antecedent: an assertion that begins an argument. The hypothesis usually follows the word if.
Conclusion/ Consequent: An ending or a sentence that closes the argument. The conclusion usually follow the word then.
Tautology: Statement that is always true
Contradiction: A statement that is always false
Beginning with a statement (p→q), the inverse (~p→~q)is formed by negating the hypothesis and negating the conclusion.
Beginning with the statement (p→q), the converse (q→p) is formed by interchanging the hypothesis and the conclusion
Beginning with the statement (p→q), then the contrapositive (~q→ ~p), formed by interchanging the resulting negation.
Two statements are logically equivalent-or logical equivalents- if they always have the truth value.
A biconditional (p↔q) is a compound statement formed by the conjunction of the conditional p→q and its converse q→p.
A valid argument uses a series of statements called premises that have known truth value to arrive at a conclusion.
The Law of Detachment states that when p→q is true and p is true, then q must be true.
The Law of Disjunctive Inference states that when p۷q is true and p is false, then q is true.
Made By: Miyu Em {@}>;--
Logic is the study of reasoning
Mathematical Sentence: A sentence is a sentence that contains a complete thought and can be judged to be true and false
Phrase: An expression that is part of a sentence
Open Sentence: Any sentence that contains a variable
Domain/ Replacement Set: Set of numbers that can replace a variable
Solution Set/ True Set: Set of all replacement that will change an open sentence or true sentence
Statement/ Close Sentence: A sentence that can be judged to be true or false
Truth Value: A close sentence has this. Either True or False
Negation: Statement with an opposite truth value of an given statement
Compound Sentence: A combination of two or more mathematical sentences formed by using the connectives not, and, or, if...then, or if and only if.
Conjunction: A compound statement formed by combining two simple statements, called conjuncts, with the word AND. The conjunction is usually formed by using the symbols
p ^ q.
Disjunction: A compound statement formed by combining two simple statements, called disjuncts, with the word OR. The disjunction is usually formed by using the symbols p v q.
Truth Table: A summary of all possible truth values of a logic statement.
Conditional: A compound statement formed by using the words if...then to combine two simple statements. The conditional if p then q is writing symbolically as p --> q.
Hypothesis/Premise/ Antecedent: an assertion that begins an argument. The hypothesis usually follows the word if.
Conclusion/ Consequent: An ending or a sentence that closes the argument. The conclusion usually follow the word then.
Tautology: Statement that is always true
Contradiction: A statement that is always false
Beginning with a statement (p→q), the inverse (~p→~q)is formed by negating the hypothesis and negating the conclusion.
Beginning with the statement (p→q), the converse (q→p) is formed by interchanging the hypothesis and the conclusion
Beginning with the statement (p→q), then the contrapositive (~q→ ~p), formed by interchanging the resulting negation.
Two statements are logically equivalent-or logical equivalents- if they always have the truth value.
A biconditional (p↔q) is a compound statement formed by the conjunction of the conditional p→q and its converse q→p.
A valid argument uses a series of statements called premises that have known truth value to arrive at a conclusion.
The Law of Detachment states that when p→q is true and p is true, then q must be true.
The Law of Disjunctive Inference states that when p۷q is true and p is false, then q is true.
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