COMPARISONS Flashcards
Define tautology in logic.
A tautology is a sentence that is true in every possible interpretation, such as ‘Either it is raining or it is not raining’.
Describe a contradiction in logical terms.
A contradiction is a sentence that is false in every possible interpretation, such as ‘It is raining and it is not raining’.
How does a contingent statement differ from a tautology and a contradiction?
A contingent statement can be true sometimes and false other times, depending on the situation.
Define equivalence in the context of propositions.
Two propositions are equivalent if they have the same truth values in all cases.
Provide an example of equivalent propositions.
P→Q and ¬P∨Q are equivalent logically and yield the same truth values.
What does it mean for a set of propositions to be jointly satisfiable?
A set of propositions is jointly satisfiable if there is at least one interpretation where they are all true.
Give an example of jointly satisfiable propositions.
An example is (P∧Q)∧(Q∨R), where both P and Q must be true, while Q or R must also hold.
Explain entailment in logical reasoning.
Entailment holds when, if the premises are true, the conclusion must also be true.
Provide an example of entailment.
If P∧Q is true, then P must also be true.
Define validity in the context of arguments.
An argument is valid if the truth of the premises guarantees the truth of the conclusion.
Illustrate validity with an example.
If P→Q and P are true, then Q must also be true.
