Propositional and predicate logic and core proof techniques from an intro discrete mathematics course.
41 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a proposition?
- A declarative statement that is either true or false, but not both.
- What is a truth value?
- The property of being either true or false.
- Define conjunction (AND) in logic.
- The logical operation where p AND q is true only when both p and q are true.
- Define disjunction (OR) in logic.
- The logical operation where p OR q is true when at least one of p or q is true.
- Define negation (NOT) in logic.
- The logical operation where NOT p reverses the truth value of p.
- What is a conditional statement?
- A statement p IMPLIES q, which is false only when p is true and q is false.
- What is a biconditional statement?
- A statement p if and only if q (p IFF q), true when p and q have the same truth value.
- What is the converse of p IMPLIES q?
- The statement q IMPLIES p.
- What is the inverse of p IMPLIES q?
- The statement (NOT p) IMPLIES (NOT q).
- What is the contrapositive of p IMPLIES q?
- The statement (NOT q) IMPLIES (NOT p).
- What is a tautology?
- A proposition that is true under every possible interpretation or truth assignment.
- What is a contradiction?
- A proposition that is false under every possible interpretation or truth assignment.
- What is a contingency?
- A proposition that is true under some interpretations and false under others.
- State De Morgan's Law for conjunction.
- NOT (p AND q) is logically equivalent to (NOT p) OR (NOT q).
- State De Morgan's Law for disjunction.
- NOT (p OR q) is logically equivalent to (NOT p) AND (NOT q).