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.
19 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a proposition, in logic?
- A declarative statement that is either true or false, but not both
- What is a logical connective?
- A symbol combining propositions, such as AND, OR, NOT, or IMPLIES
- What does the AND (conjunction) connective require for a true result?
- Both propositions must be true
- What does the OR (disjunction) connective require for a true result?
- At least one of the propositions must be true
- What does the NOT (negation) connective do?
- Reverses the truth value of a proposition
- What is a conditional statement (implication)?
- A statement of the form 'if p then q', false only when p is true and q is false
- What is a biconditional statement?
- 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?
- The statement formed by swapping the hypothesis and conclusion (if q then p)
- What is the contrapositive of a conditional statement?
- 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?
- They share the same truth table for all possible values of p and q
- What is a truth table?
- A table listing the truth value of a compound proposition for every combination of inputs
- What is a tautology?
- A compound proposition that is always true, regardless of the truth values of its parts
- What is a contradiction, in logic?
- A compound proposition that is always false, regardless of its parts' truth values
- What is logical equivalence?
- Two propositions that have identical truth values in every possible case
- What are De Morgan's laws?
- 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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