How to build and read truth tables for logical connectives such as AND, OR, and the conditional.
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- What is a truth table?
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A table showing all possible combinations of truth values for propositions and their results under logical operations.- When is a conjunction (AND) true?
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When both propositions are true.- Conjunction: true AND true = ?
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true- Conjunction: true AND false = ?
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false- Conjunction: false AND false = ?
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false- When is a disjunction (OR) true?
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When at least one proposition is true.- Disjunction: true OR true = ?
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true- Disjunction: true OR false = ?
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true- Disjunction: false OR false = ?
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false- What does the NOT operator do?
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Reverses the truth value of a proposition.- NOT true = ?
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false- NOT false = ?
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true- What is a conditional?
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A logical statement asserting that if the antecedent is true, then the consequent must be true.- When is a conditional false?
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Only when the antecedent is true and the consequent is false.- Conditional: true > false = ?
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false
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