---
# System prepended metadata

title: Mini-Quiz May 18
tags: [' lt-quiz', 225-spr22, ' mth225']

---

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

# Mini-Quiz May 18

:::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 3, 5 and 6**. You may attempt Learning Target 3 and **exactly one** of Learning Targets 5 or 6. You may not do both Learning Targets 5 *and* 6 (because this is a "mini" quiz). 


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 3

:::warning
(**CORE**) Given a conditional statement, I can state its hypothesis, conclusion, negation, converse, inverse, and contrapositive. 
:::

Consider the conditional statement: *If the user enters a wrong number, then an error message appears.* 

1. State the **hypothesis** of this statement. 
2. State the **conclusion** of this statement. 
3. State the **converse** of this statement. 
4. State the **inverse** of this statement.
5. State the **contrapositive** of this statement.
6. State the **negation** of this statement (without simply putting "Not" or "It is not the case that" in the front of the statement). 

**Success criteria:** All answers are given in clear and correct English (*not* in symbolic notation). The negation and contrapositive must be correct, and no more than one error is allowed in the others. 

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:::danger
Remember: Do **only one** of the following two Learning Targets. 
:::

## :new: Learning Target 5

:::warning
I can use a truth table to decide if a statement is a tautology or contradiction, or to determine if two statements are logically equivalent. 
:::

1. Use truth tables to determine whether the statements $p \rightarrow (\neg q)$ and $(\neg q) \rightarrow (\neg p)$ are logically equivalent or not. 
2. Use a truth table to determine whether the statement $(p \wedge q) \rightarrow (p \vee q)$ is a tautology. 

**Success criteria:** All truth tables have the correct number of rows with no duplicated rows. All intermediate columns are shown. No more than three total errors are permitted. (If you make a mistake in an intermediate column but the rest of the row is correct given that mistake, then the mistake only counts once.) The answers (about whether the statement is a tautology, and about whether the two statements are logically equivalent) are clearly indicated. 


## :new: Learning Target 6

:::warning
I can determine the truth value of a predicate at a specific input, and given a quantified predicate I can state its negation and its truth value.
:::

Consider the predicates: 

- $P(x)$: $x^2$ is odd
- $Q(x)$: The tens digit of $x$ is even 

The domain of each predicate is the set of all *positive* integers. 

1. For each of the following, state whether the expression is **True**, **False**, or **Undetermined**.  
    (a) $P(121)$
    (b) $Q(121)$
    (c) $\exists x P(x)$ 
    (d) $\exists y (\neg P(x))$ 
    (e) $\forall z Q(z)$
2. State the negation of the following without just inserting "Not" or "it is not the case that": 
    (a) $\exists x Q(x)$ 
    (b) Every square is a rectangle. 
    (c) Some triangles are equilateral. 
    
    
**Success criteria:** All the answers in the first item are correct. At least two of the three partsof the second item are correct. 