A. Explain why the given described is an onto mapping.

B. Create a own real-world example of an onto mapping without using a math formula
o Explain what set constitutes the domain.
o Explain what set constitutes the codomain.
o Explain what relationship exists between the elements in the domain and the elements in the range.

C. Explain how we could change the domain of the mapping in part B so that the mapping would no longer be onto.

D. Explain how we could change the codomain of the mapping in part B so that the mapping would no longer be onto.

Solution Preview

A. An onto mapping is one in which some member of the domain is mapped to every member of the range. As stated the Given statement is NOT onto if students are in the domain and mentors are in the range. On the other hand, if mentors are in the domain and students are in the range, then every member in the range (all students) is included in the mapping. In that case, the mapping is ...

... Yes, they can be classified as functions because each element in the domain has just one image in the codomain, which satisfies the definition of a function. ...

... map smaller set to bigger sets: F: onto means codomain = range. ...Domain : (-infinity, infinity) because, this is bijective function,hence, Range: (-infinity ...

... of the domain are mapped to an element x −1 of the codomain, band for every element y in the codomain, there exists an x in the domain (1, ∞) such 1 1 = y ...

... are invariant under homeomorphisms, the theorem equally applies if the domain is not the ... function known as a retraction: every point of the codomain (in this ...