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What is Modus Ponens rule? 学び始める
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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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学び始める
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A declarative statement that is either true or false but not both.
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学び始める
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what are the propositional variables? 学び始める
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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? 学び始める
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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? 学び始める
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what is the conjunction (and) connective symbol? 学び始める
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What is the disjunction (or) connective symbol) 学び始める
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what is the connective symbol for implication (if-then) 学び始める
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What is the biconditional (if and only if) connective symbol? 学び始める
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what order are connective symbols considered in? 学び始める
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1) brackets, 2) negation, 3) conjunction dissjunctive, 4) implication bicnditional
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what is a tautology statement? 学び始める
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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 学び始める
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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? 学び始める
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define logical equivalent 学び始める
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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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学び始める
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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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学び始める
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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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学び始める
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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? 学び始める
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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 学び始める
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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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学び始める
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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 学び始める
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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 学び始める
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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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