Math 107 Quiz 5, SS, AY 2023-2024

Which of the following is not a one-to-one function?

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• Schroeder-Bernstein Theorem

• Cantor’s Theorem

• Continuum Hypothesis

• Axiom of Infinity

• It is countable.

• It is denumerable.

• It is empty.

• It is uncountable.

If every nonempty subset of a set has a smallest element in the ordering, then it is called:

• Well-ordered Sets

• Transitive Sets

• Successor Sets

• Equipotent Sets

What do you call the range of the restriction of a function by a set?

• The image set of the set under the function

• The image of the inverse of the function by the set

• The composition of the function and the set

• The inverse of the function

Let 𝑀={(𝑥,𝑦) | 𝑥 𝑖𝑠 𝑎 𝑝𝑎𝑟𝑒𝑛𝑡 𝑜𝑓 𝑦} and
𝑁={(𝑎,𝑏) | 𝑎 𝑖𝑠 𝑎 𝑠𝑖𝑏𝑙𝑖𝑛𝑔 𝑜𝑓 𝑏}. If 𝑀 and 𝑁 are relations on the set of people 𝐴, what is 𝑀 ∘ 𝑀?