D420 Discrete Math: Functions and Relations - Set 2 - Part 3

Correct Answer: A function where every element in the codomain has at least one preimage

A surjective function is one where every element in the codomain is the image of at least one element from the domain.

Correct Answer: A bijection

A bijection is a function that is both injective (one-to-one) and surjective (onto).

Correct Answer: A subset of AB

A binary relation from set A to set B is a subset of the Cartesian product AB, where elements from A are related to elements from B.

Correct Answer: (a,a)A for all aA

A reflexive relation requires that every element in the set is related to itself, meaning (a,a)A for all aA.

Correct Answer: If a is related to b and b is related to a, then a=b

An antisymmetric relation is one where if a is related to b and b is related to a, then a must equal b.

Correct Answer: If a is related to b and b is related to c, then a is related to c

A transitive relation is one where if one element is related to a second and the second is related to a third, the first is related to the third.

Correct Answer: The set of elements that are related to a given element by an equivalence relation

An equivalence class is the set of elements that are related to a given element by an equivalence relation.

Correct Answer: A collection of subsets of the set that are pairwise disjoint and whose union is the original set

A partition of a set divides the set into non-overlapping subsets whose union equals the original set.

Correct Answer: A function where multiple elements in the domain map to the same element in the codomain

A function is not injective if two or more distinct elements in the domain map to the same element in the codomain.

Correct Answer: All of the above

The composition of two injective functions is injective, the composition of two surjective functions is surjective, and the composition of two bijective functions is bijective.