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What is Modus Ponens rule? 开始学习
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if this then that or " if X then Y" is true and "X" is true => so "Y " must be true
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开始学习
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A declarative statement that is either true or false but not both.
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开始学习
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what are the propositional variables? 开始学习
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Each propositional variable has one of two truth values: true or false
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what is a compound statment? 开始学习
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A compound statement is a sentence that consists of two or more statements separated by logical connectors.
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what is the negation (not) connective symbol? 开始学习
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what is the conjunction (and) connective symbol? 开始学习
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What is the disjunction (or) connective symbol) 开始学习
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what is the connective symbol for implication (if-then) 开始学习
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What is the biconditional (if and only if) connective symbol? 开始学习
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what order are connective symbols considered in? 开始学习
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1) brackets, 2) negation, 3) conjunction dissjunctive, 4) implication bicnditional
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what is a tautology statement? 开始学习
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true for all possible values of its propositional variables is called a tautolog
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what is a contradiction statment 开始学习
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false for all possible values of its propositional variables is called a contradiction
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what is the symbol for logical equivalence? 开始学习
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define logical equivalent 开始学习
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Two statements are said to be logically equivalent,≡, if they have identical truth values for each possible value of their statement variables. (Corresponds to = with numbers)
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开始学习
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refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.
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开始学习
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"multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.
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开始学习
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The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection of two sets is equal to the union of their complements.
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conditional statement consists of two parts, a hypothesis the “if” clause and conclusion the “then” clause. For instance “If it rains, then they cancel school.” "It rains" is the hypothesis. "They cancel school" is the conclusion. what is the converse? 开始学习
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To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."
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conditional statement consists of two parts, a hypothesis the “if” clause and a conclusion the “then” clause. For instance, “If it rains, then they cancel school.” "It rains" is the hypothesis. "They cancel school" is the conclusion. what is the inverse 开始学习
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To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”
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开始学习
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To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain
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define sufficient condition 开始学习
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a condition that must be satisfied for a statement to be true and without which the statement cannot be true
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define necessary condition 开始学习
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a condition that must be present for an event to occur. A sufficient condition is a condition(s) that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.
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