Logic – a system of reasoning that Flashcards
What is Logic?
Logic is a system of reasoning that allows inferences to be drawn from facts.
What is a Proposition?
A proposition is a declarative sentence that is either true or false, but not both.
Example: “Luzon is an island in the Philippines.” This is a TRUE proposition.
What is a Conjunction?
A conjunction is an ‘AND’ statement in mathematics. A conjunction of two statements is true only when both statements are true.
What is a Disjunction?
A disjunction is an ‘OR’ statement in mathematics. A disjunction is false if and only if both statements are false; otherwise it is true.
What is Negation?
Negation is a ‘NOT’ statement in mathematics. It is a statement with the opposite truth value.
What is a Conditional?
A conditional (or implication) is a logical compound statement in which p implies q. The statement is only false when p is true but q is false.
What is a Biconditional?
A biconditional is true when both have the same truth value.
Example: If p and q are both true, then the statement is true. Same goes if p and q are both false.
What is an Exclusive-or?
An exclusive-or statement is true if you are either one but not both. P and q cannot be the same.
Example: I am a dog or I am a cat.
What are Truth Values of a proposition?
The truth value of a proposition is a determination of whether the proposition is true (T) or false (F).
Example: Proposition: “The sun rises in the east.”
What are Conditional Propositions?
Conditional propositions are ‘if-then’ expressions. They are false only when p is true and q is false, and true in all other situations.
Example: “If I study, then I will pass the test.”
What is the Converse of p-q?
The converse of p-q is a conditional proposition in which ‘p implies q’ becomes ‘q implies p’.
Example: Original: “If it rains, the ground is wet.” Converse: “If the ground is wet, it rained.”
What is the Inverse of p-q?
The inverse of p-q is a conditional proposition in which ‘p implies q’ becomes ‘not p implies not q’.
Example: Original: “If it rains, the ground is wet.” Inverse: “If it does not rain, the ground is not wet.”
What is a Contrapositive?
A contrapositive is a conditional proposition in which ‘p implies q’ becomes ‘not p implies not q’.
Example: Original: “If it rains, the ground is wet.” Contrapositive: “If the ground is not wet, it did not rain.”
What is a Tautology?
A tautology is a proposition that is always true.
Example: “It is either raining or not raining.”
What is a Contradiction?
A contradiction is a proposition that is always false.
Example: “It is both raining and not raining.”