Discrete Math for Computer Science, unit: Logic and Propositions. Core concepts, terminology, and worked-example cues a college student meets for this unit, building on prior units without repeating them. Front: a term, concept, or short problem cue. Back: the definition, explanation, or answer.
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- What is a proposition, in logic?
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A declarative statement that is either true or false, but not both- What is a logical connective?
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A symbol combining propositions, such as AND, OR, NOT, or IMPLIES- What does the AND (conjunction) connective require for a true result?
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Both propositions must be true- What does the OR (disjunction) connective require for a true result?
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At least one of the propositions must be true- What does the NOT (negation) connective do?
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Reverses the truth value of a proposition- What is a conditional statement (implication)?
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A statement of the form 'if p then q', false only when p is true and q is false- What is a biconditional statement?
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A statement of the form 'p if and only if q', true when p and q have the same truth value- What is the converse of a conditional statement?
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The statement formed by swapping the hypothesis and conclusion (if q then p)- What is the contrapositive of a conditional statement?
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The statement formed by negating and swapping both parts (if not q then not p)- Why is the contrapositive logically equivalent to the original conditional?
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They share the same truth table for all possible values of p and q- What is a truth table?
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A table listing the truth value of a compound proposition for every combination of inputs- What is a tautology?
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A compound proposition that is always true, regardless of the truth values of its parts- What is a contradiction, in logic?
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A compound proposition that is always false, regardless of its parts' truth values- What is logical equivalence?
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Two propositions that have identical truth values in every possible case- What are De Morgan's laws?
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Rules stating not(p and q) equals (not p) or (not q), and not(p or q) equals (not p) and (not q)
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