Logic, set theory, combinatorics, and graph theory basics from a discrete math course.
37 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a tautology?
- A statement that is true in all possible truth value assignments; always true regardless of the truth values of its variables.
- What is a contradiction?
- A statement that is false in all possible truth value assignments; always false regardless of the truth values of its variables.
- De Morgan's law: negation of (P and Q) equals what?
- (not P) or (not Q)
- De Morgan's law: negation of (P or Q) equals what?
- (not P) and (not Q)
- What is the contrapositive of 'if P then Q'?
- If not Q then not P. It is logically equivalent to the original statement.
- What is a logical equivalence?
- Two statements are logically equivalent if they have the same truth value in every possible interpretation or truth assignment.
- What is the difference between conjunction and disjunction?
- Conjunction (and) is true only when both operands are true. Disjunction (or) is true when at least one operand is true.
- What does it mean for a statement to be satisfiable?
- A statement is satisfiable if there exists at least one truth value assignment that makes it true.
- What is a truth table?
- A table that lists all possible truth value assignments for variables in a logical statement and the resulting truth value of the statement.
- The negation of 'all A are B' is what?
- There exists at least one A that is not B, or equivalently, some A are not B.
- What is the cardinality of a set?
- The number of elements in the set, denoted |A| for set A.
- What does the union of two sets A and B contain?
- All elements that belong to A or B or both, denoted A union B.
- What does the intersection of two sets A and B contain?
- All elements that belong to both A and B, denoted A intersect B.
- What is the complement of a set A in universal set U?
- All elements in U that are not in A, denoted A' or U minus A.
- What is the Cartesian product of sets A and B?
- The set of all ordered pairs (a, b) where a is in A and b is in B, denoted A times B.