| Antecedent | The term of a conditional claim that lies between the "if" and the "then." The proposition asserts that if the antecedent were the case, the consequent would then follow.
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| Biconditional | A proposition of the form "A if and only if B."
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| Categorical proposition | A proposition that is expressed in one of four forms: "All A is B," "No A is B," "Some A is B," of "Some A is not B."
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| Compound proposition | A proposition that contains any of the five logical connectives ("and," "or", "not, "ifÉthen," or "if and only if"). For example, "Either the cow is in the yard or that's a Hollywood prop."
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| Conditional claim | A proposition of the form "If A then B" or its variations.
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| Conditional claims | Propositions of the form "If A then B" or "B only if A."
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| Conjunct | One member of a conjunction. Both A and B are conjuncts of the claim "A and B."
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| Conjunctions | Propositions that can be expressed in the form "A and B."
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| Consequent | The term of a conditional claim that follows the "then" and is said to be the effect that follows if the antecedent condition were true.
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| Contingent claims | Propositions that are not necessarily true or false, but are dependent on what is going on in the world to determine the truth-value. This would include claims for which the truth-value is unknown.
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| Contradictions | Propositions that are always false or false by definition.
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| De Morgan's Laws | These are two special forms of negations: "Not both A and B" and "Neither A nor B." With the "Not both" construction, one of the choices is being denied--either the first option or the second one. With a "neither... nor..." construction, both options are being denied, the first choice and the second one.
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| Disjunct | One member of a disjunction. Both A and B are disjuncts of the claim "Either A or B."
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| Disjunctions | Propositions that can be expressed in the form "Either A or B."
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| Equivalence | Propositions of the form "A if and only if B."
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| Exportation | This rule of replacment allows you to restructure a conditional claim with a conjunction in the antecedent. The second conjunct in the antecedent is exported to the consequent where it starts a new chain: "If A and B then C" is equivalent to "If A then, if B then C."
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| Logical connectives | The terms that make a proposition compound. These are: "and," "either/or," "if/then," "if and only if," and "not").
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| Material Implication | One of the rules of replacement. This asserts "If A then B" is equivalent to "Either not A or B."
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| Necessary | "P is necessary for Q" asserts that Q won't happen without P. That is, if you don't have P, you won't have Q. So if you have Q, you must also have P.
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| Negations | Propositions that can be expressed in the form "Not A."
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| Only | The term "only" is used to restrict and, thus, functions as an exclusion. "Only A is B" is equivalent to "If not A then not B" which is equivalent to "All B is A."
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| Only if claims | Propositions that can be expressed in the form "A only if B," which are equivalent to "All A is B." "If A then B" and "If not B then not A."
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| Particular | Particular propositions are not universal. They assert or deny a characteristic applies to at least one but not all the members of the class in question. These are I and O claims ("Some A is B" and "Some A is not B").
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| Proposition | A proposition, or claim, asserts something is or is not the case (e.g., "This is Tuesday," "All cats are animals," "Some cats are not tigers," etc.).
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| Quality | The quality of a proposition is either positive (A and I claims) or negative (E and O claims). The quality answers the question "Are you affirming or negating?"
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| Quantity | The quantity of a proposition is either universal (A and E claims) or particular (I and O claims). Quantity answers the question "How many?"
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| Simple proposition | A simple proposition is one that is at the atomic level--that is, it does not contains any of the logical connectives "and," "or", "not, "ifÉthen," or "if and only if." For example, "Some dogs are gentle animals."
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| Sufficient | "P is sufficient for Q" asserts that Q will happen whenever P occurs. In other words, "P is sufficient for Q" is equivalent to "If P then Q."
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| Tautologies | Propositions that are always true or true by definition.
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| The only | "The only P is Q" is equivalent to "Only Q is P."
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| Translation | That which results from symbolizing a proposition using logical connectives and variables.
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| Transposition | One of the rules of replacement. This asserts "If A then B" is equivalent to "If not B then not A." In other words you can transpose the antecedent and consequent--but both must then change to their opposites (positive-negative and vice versa).
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| Universal | Universal propositions are "all or nothing" claims (A and E claims). They can be expressed "All A is B" or "No A is B."
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| Unless | Propositions of the form "P unless Q" can be expressed as either a conditional claim or a disjunction. As a conditional claim it can be written, "If not Q then P."
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| Variable | A letter of the alphabet used to represent a proposition. For example, "If Joe runs the marathon, he'll be tired tonight." Variable "J" and "T" could be used to symbolize the proposition as: J → T.
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