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