---
tags: 225-spr22, mth225, lt-quiz
---

# Mini-Quiz May 24

:::info
This is a **mini-quiz**, designed to give you an attempt at **one Learning Target** of your choice from among the more recent ones we've covered, done **quickly** and **in class**.

This mini-quiz contains problems for **Learning Targets 8 and 10**. You may do just one, or both; or if you prefer to practice some more and try again this week, do nothing and just take the main Quiz on Thursday.

Work the problems you select out on paper or in a notes app, export the work to PDF (one PDF per Learning Target) and upload it to the appropriate assignment folder on Blackboard just as in the case of a full Quiz.

**Your work is due by 2:30pm.** No submissions will be accepted after that time.
:::

## Learning Target 8

:::warning
(**CORE**) I can find the cardinality, power set, and complement of a set; and I can find the intersection, union, difference, and Cartesian product of two sets.
:::

Consider the sets:
$$A = \{1, 2, 4, 8, 16\} \qquad B = \{x^2 \, : \, x \in \{1,2,3\} \} \qquad C = \{4, 8, 12, 16, 20\}$$
The universal set $U$ is the set $\{1, 2, 3, \dots, 20\}$.
Determine each of the following. **If the answer is a set, write it in roster notation**.

1. $A \setminus C$
2. $A \cup B$
3. $A \cap C$
4. $A \times \{0,100\}$
5. $|{\cal{P}} (B)|$ (where ${\cal{P}} (B)$ is the power set of $B$)
6. $\overline{C}$ (the complement of $C$)

**Success criteria:** At least five of the six items have correct responses, and no more than two simple errors are present.

## :new: Learning Target 10

:::warning
I can determine if a function is injective, surjective, and/or bijective.
:::

Below are three functions with their domains and codomains specified. For each one, classify it as

* Injective but not surjective,
* Surjective but not injective,
* Neither injective nor surjective, or
* Bijective.

If a function *does* have a property you do not have to explain why; but if a function *fails* to have a property, you should explain why in as specific of terms as possible. (Do not just state the definition of the property or give a vague reinterpretation of that definition, but refer to specific elements or other characteristics.)

1. $f: \mathbb{N} \rightarrow \mathbb{N}$ defined by $f(a) = a + 2$
2. $g: \mathbb{R} \rightarrow \mathbb{Z}$ defined by $g(x) = \lfloor x \rfloor$, the "floor function" (takes a real number and rounds it down)
3. $h: \{1,2,3,4,5\} \rightarrow \{a,b,c,d,e\}$ given by the two-line diagram:
$$\begin{pmatrix}
1 & 2 & 3 & 4 & 5 \\
a & b & a & c & e
\end{pmatrix}$$

**Success criteria:** At least two of the three items has a correct answer that is clearly indicated, accompanied by a correct, clearly written explanation (if the function is not bijective). *Both* the answer and the explanation must be clear, correct, and easy to understand and the explanation must be given in precise terms.

:::info
**About the explanation:** You only need to explain if a function *isn't* injective or *isn't* surjective. If the function is bijective, no explanation is necessary at all (but the answer has to be right).

The explanation needs to be *as specific as possible*. For example you can't just say "There's a collision" if you think a function is not injective. Be specific.
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