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# System prepended metadata

title: 'Answer Key: Learning Target Quiz 2'
tags: [mth225]

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tags: mth225
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# Answer Key: Learning Target Quiz 2

:::info
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:::

## CA.1

1. Binary: 1101001. Octal: 151.
2. Decimal: 185. Hexadecimal: B9.
3. 380
4. 1001 0100


## CA.2

1. 101011000
2. 10000010
3. 100111
4. Quotient = 1010, remainder = 10

## L.1

1. 
* Hypothesis: $P \vee Q$, conclusion: $R$
* Negation: $(P \vee Q) \wedge (\neg R)$ 
* Converse: $R \rightarrow (P \vee Q)$ 
* Contrapositive: $(\neg R) \rightarrow \neg (P \vee Q)$ 

2. 
* Hypothesis: Apple comes out with a new iPad; Conclusion: I won't buy a laptop
* Negation: Apple came out with a new iPad and I did buy a laptop. 
* Converse: If I don't buy a laptop, Apple came out with a new iPad. 
* Contrapositive: If I do buy a laptop, Apple didn't come out with a new iPad. 


## L.2

1.
| $P$ | $Q$ | $P \vee Q$ | $\neg (P \vee Q)$ |
   | --- | --- | ---------- | ----------------- |
   |  T  |  T  | T | F | 
   |  T  |  F  | T | F |
   |  F  |  T  | T | F | 
   |  F  |  F  | F | T |
   
| $P$ | $Q$ | $\neg P$ | $\neg Q$ | $(\neg P) \vee (\neg Q)$ |
   | --- | --- | ---------- | ----------------- | ---- | 
   |  T  |  T  | F | F | F 
   |  T  |  F  | F | T | T
   |  F  |  T  | T | F | T
   |  F  |  F  | T | T | T 
   
So the two statements are NOT logically equivalent. 

2. 
| $P$ | $Q$ | $R$ | $\neg P$ | $Q \rightarrow R$ | $(\neg P) \wedge (Q \rightarrow R)$ | 
| :--: | :--: | :--: | :--: | :--: | :--: | 
| T | T | T | F | T | F | 
| T | F | T | F | T | F |
| F | T | T | T | T | T | 
| F | F | T | T | T | T | 
| T | T | F | F | F | F | 
| T | F | F | F | T | F | 
| F | T | F | T | F | F | 
| F | F | F | T | T | T | 

## L.3 

1. $P(2)$ false, $P(11)$ true, $Q(2)$ true, $Q(20)$ true. 
2. (a) False because $P(2)$ is false. 
   (b) True because $P(11)$ is true. 
   (c) True because $Q(2)$ is true. 
3. There is at least one GVSU student who did not grow up in Michigan. 

## SF.1 

1.(a) $\{\dots, -18, -8, 2, 12, 22, 32, \dots \}$
  (b) $\{1,2,3,4,5,6,7\}$
  (c) $\{3, 11, 17\}$
2. Many correct answers; one is $\{n \in \mathbb{N} \, : \, n \ \% \ 3 = 2\}$. 
3. (a) True 
   (b) True 
   (c) False 
   (d) False 
   (e) True 
   (f) False (because $2 \ \% \ 2 \neq 1$)
   (g) False (the set on the right is $\{4, 8, 12\}$)
   (h) True 
   
Note: On part 3, each incorrect answer was treated like a "simple" error for the entire problem, i.e. you are allowed two such answers before needing to try again. 