Truth Tables Flashcards
What is the logical connective for conjunction, and what does it represent?
The logical connective for conjunction is a dot (*), representing the combination of two claims with the word ‘and’.
How is a conjunctive proposition evaluated according to the rule of conjunction?
A conjunctive proposition is true only when both the first conjunct and the second conjunct are true; otherwise, the proposition is false.
Define a disjunctive proposition and its logical connective.
A disjunctive proposition contains the binary words ‘either/or’, and its logical connective is a wedge (v).
According to the rule of disjunction, when is a disjunctive proposition false?
A disjunctive proposition is false only when both the first disjunct and the second disjunct are false; otherwise, it is true.
What is a material implication, and how is it symbolized?
A material implication involves making a conditional claim within a compound proposition, with the logical connective represented by a horseshoe (⊃).
Explain the rule of material implication under the truth table.
A proposition is false only when its antecedent is true and its consequent is false; otherwise, the proposition is true.
What does a biconditional proposition entail, and what symbol represents it?
A biconditional proposition relates two statements that are true or false simultaneously, symbolized by a triple bar (≡).
According to the rule of biconditional (material equivalence), when is a proposition true?
A proposition is true only when the first material biconditional is equivalent in truth value with the second material biconditional; otherwise, it is false.
What is the logical connective for negation, and what does it signify?
The logical connective for negation is a tilde (~), indicating the denial or opposite of a statement.
How is the negation of a true proposition evaluated under the truth table?
The negation of a true proposition results in its opposite or contradiction, making it false.
What does symbolization in logic involve?
Symbolization in logic entails reducing arguments expressed in words into specific variables or symbols.
Provide an example of symbolization for a logical argument.
For instance, the argument “If Angola achieves stability, then both Botswana and Chad will adopt more liberal policies. But Botswana will not adopt more liberal policies. Therefore, Angola will not achieve stability” can be symbolized as A ⊃ (B * C), ~B, ∴ ~A.
Explain the importance of truth tables in promoting critical reasoning.
Truth tables provide a systematic approach to evaluating the truth value of propositions, enhancing critical reasoning skills in logic.
