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Definition
| a branch of formal, deductive logic in which the basic unit of thought is the proposition |
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| a statement (sentence with a truth value) |
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| 3 tools used in Propositional Logic |
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Definition
Truth Tables (Unit 1)
Formal Proofs (Unit 2)
Truth Trees (Unit 3) |
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| truth-functional proposition |
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Definition
| a proposition whose truth value depends on the truth value of its component parts |
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| a proposition with only one component part (NO logical operators) |
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| a proposition with more than one component part or a modified (negated) part (MUST have at least one logical operator) |
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| words which combine or modify simple propositions to make compound propositions |
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Definition
-upper case letter
-represents a single, given proposition |
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Definition
-lower case letter
-represents any proposition |
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| a listing of the possible truth values for a set of one or more propositions |
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| a truth table that completely defines its operations on a minimum number of variables (shown in Appendix A) |
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Definition
~ "not"
logical operator that denies or contradicts a proposition |
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Definition
• "and"
logical operator that joins 2 propositions (conjuncts) and is true if and only if both propositions are true |
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ν "or"
logical operator that joins 2 propositions (disjuncts) and is false if and only if both propositions are false |
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| 4 steps to find truth values for complicated propositions |
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Definition
1. draw horizontal line, place all variables on left side, list all possible combinations of T & F beneath
2. if any variables are negated, add columns for those truth values
3. add columns for anything inside parentheses
4. add columns for each operator until the compound proposition is completed |
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Term
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Definition
⊃"If...then"
logical operator that asserts that one compound part (the antecedent) implies the other (the consequent). It is false if and only if the antecedent is true and the consequent is false (aka hypothetical, material implication) |
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Definition
| the proposition that follows the "If" in a conditional proposition |
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| the proposition that follows the "then" in a conditional proposition |
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| 5 statements equivalent to p ⊃ q |
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Definition
If p then q
p implies q
p only if q
when p, q
p is sufficient for q |
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| 2 statements equivalent to q ⊃ p |
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Definition
p if q
p is necessary for q |
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| translate p unless q and unless p, q |
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Definition
| p unless q = ~q ⊃ p unless p, q=~p ⊃ q |
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Term
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Definition
≡ "if and only if"
logical operator that is equivalent to the conjunction of a conditional and its converse: (p ⊃ q) •(q ⊃ p)
it is true when both parts have the same truth value and false when their truth values are different |
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