1/9
These flashcards cover key vocabulary and definitions related to binary relations from the lecture notes on logic and algorithms.
Name | Mastery | Learn | Test | Matching | Spaced |
---|
No study sessions yet.
Reflexivity
A relation R on set A is reflexive if ∀x ∈ A, (x, x) ∈ R.
Counterexample
An example that disproves a proposition or relation.
Symmetry
A relation R is symmetric if ∀x, y ∈ A, if (x, y) ∈ R then (y, x) ∈ R.
Anti-symmetry
A relation R is anti-symmetric if for all x, y ∈ A, if x ≠ y then (x, y) ∈ R implies (y, x) ∉ R.
Transitivity
A relation R is transitive if ∀x, y, z ∈ A, if (x, y) ∈ R and (y, z) ∈ R, then (x, z) ∈ R.
Relation
A relation R on set A is a subset of the Cartesian product A × A.
Domain
The set of all possible inputs for a function or relation.
Modulus
The operation that finds the remainder after division of one number by another.
Proof by exhaustion
A method of proving a statement by checking all possible cases.
Universal generalization
The principle that states if a property holds for all members of a set, it can be generalized for the set.