Skip to main content

# 2.E: Chapter Two (Exercises)

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$
##### Exercise $$\PageIndex{1}$$: Vagueness vs Ambiguity

Is each inference an illustration of vagueness or ambiguity?

A. She said “go blow your nose” and I’ve been trying for an hour to blow on my nose. It’s tricky.

B. I don’t think I lied, I said “I’ll be there to help you if you need it” and you didn’t really need help this time since you clearly survived without my help.

C. Teacher, you said to do the test “without help” and Jesus is using a pencil to complete the test. That’s helping him do it!

D. You said not to tattle, so when I saw the murderers running away from their victim I remained tight-lipped as ever.

E. Uggh. I said I wanted regular blonde hair, not platinum blonde hair! You messed my hair up.

F. The physics teacher said that on a level plane it’s indeterminate which way a stationary object will start to roll, but I’ve been setting this ball down carefully on the floor of this airplane and it has been rolling backwards every time!

G. Of course humans can fly. I just flew to Los Angeles last week!

H. She said “I’ll meet you inside,” so I went deep inside my soul in search of her, but never found her.

I. "As I was leaving this morning, I said to myself, 'The last thing you must do is forget your speech.' And, sure enough, as I left the house this morning, the last thing I did was to forget my speech."– Rowan Atkinson

J. You said we’d meet early today, but I’ve been waiting here since 5 am and you just now showed up at 7 am!

K. “I didn’t go to the party because Shamik was there.”

“Oh, so you went to sample the appetizers?”

L. I’m not a very good student, I only have a 3.87 GPA.

M. You’re so rich! You have a working refrigerator.

N. It’s so cold outside today, it’s like 50 degrees.

O. “Call me a taxi, please.”

“Okay, you’re a taxi!”

P. Union demands increased unemployment. -newspaper headline

Q. My mom says I don’t listen to her. Well I do listen to her, I just don’t do what she tells me to do!

##### Exercise $$\PageIndex{2}$$: Intensional Meaning and Extensional Meaning

Is each of the following series, determine whether the extension is increasing or decreasing and then determine whether it has more intensional information (it’s getting more specific) or decreasing intensional information (it’s getting less specific). “No change” is also an option for both dimensions (intension and extension).

A. Indian food, North Indian food, Masala dishes, Paneer Masala.

B. My rude neighbor guy, rude guys, rude people, people.

C. The Moon, moons, moons in our solar system, natural satellites (any natural object orbiting a planet) in our solar system, natural satellites.

D. Jimmy Carr (an English comedian), English comedians, British comedians, comedians.

E. Earth, planets in our solar system with intelligent life, the planet on which Captain America: Civil War takes place, the planet that is home to almost all living human beings.

F. Pink Floyd, rock groups from the 70’s and 80’s, English-speaking rock groups, rock groups

##### Exercise $$\PageIndex{3}$$: Types of Definitions

For each definition, determine the answer to each of the following questions: a) Is it Stipulative or Descriptive? b) Is it too broad or too narrow, or is it apt? c) Is it argumentative or Neutral?

A. An immigrant is any person who comes into a country for a stay that is longer than two months without being a citizen of the country.

B. An immigrant is someone like Natalie Portman, Gal Gadot, John Oliver, or James McAvoy.

C. Furniture is a human-made object used to store or hold things; or sit or lay on.

D. A ruler is a straight and rigid device used to measure lengths.

E. A criminal is someone who has committed a crime.

F. A Russian is someone who is not to be trusted.

G. A communist is someone like Stalin, Pol Pot, Mao, or Kim Jong Un.

H. A wristwatch is a time piece made to be worn around one’s wrist.

I. A smart device is any device with the ability to connect to the internet.

##### Exercise $$\PageIndex{4}$$: Fallacy of Equivocation

Explain how this is equivocation...

A. You said you would meet me at the park, but we’ve already met—years ago in fact—so I don’t think we should plan to meet in the future.

B. That bumper sticker says “the cost of freedom is great,” which is weird because I never think of war as all that great. It’s pretty awful.

C. Peter: Let’s go to the gym to do a bit of working out.

Tamil: Okay, but you won’t need your running shoes at the climbing gym, you should grab your climbing shoes instead and just wear street shoes on the way there.

##### Exercise $$\PageIndex{5}$$: Necessary and Sufficient Conditions

Fill in each blank with either Necessary and Sufficient, Necessary but not Sufficient, Sufficient but not Necessary, or Neither Necessary nor Sufficient.

A. Giving birth a baby is a _______ condition to becoming a mother.

B. Eating spicy foods is, for many people, a _______ condition for having gastro-intestinal problems.

C. Drinking milk is, for lactose-intolerant people, a ________ condition for having gastro-intestinal problems.

D. Flying in a plane is a ________ condition for getting from California to Hawaii in under 24 hours.

E. Dropping a sick beat is a ___________ condition for rapping.

F. Being alive is a ________ condition for running for President.

G. Eating at least every three weeks is a ___________ condition for staying alive (for humans).

H. Having an ear of corn in your possession is a _______________ condition for making corn bread.

I. Selling drugs in front of a police officer is, in normal circumstances, a ___________ condition for being arrested

J. Being a set of bound pages containing a more or less unified piece of writing or collection of writings is a _____________ condition for being a book.

K. Putting fruit, yogurt, and milk in a blender and blending until smooth is a ________ condition for making a smoothie.

This page titled 2.E: Chapter Two (Exercises) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Andrew Lavin via source content that was edited to the style and standards of the LibreTexts platform.

• Was this article helpful?