Explain how to read a table such as Table $1.1$ and how to show the information in a Venn diagram.

Briefly explain the idea of strength and how it applies to inductive arguments. Can an inductive argument prove its conclusion true? Can an inductive argument be valid? Can it be sound?

Find out the dimension of below object, and state whether or not it is a fractal. In measuring the length of the object, when you reduce the length of your ruler by a factor of $5$, the number of length elements increases by a factor of $5$.

Explain how to draw a Venn diagram for three overlapping sets. Discuss the types of information that can be shown in such diagrams.

Choose an issue that you feel strongly about, and create an argument in support of your position. Is your argument inductive or deductive? Evaluate your argument.

Find out the dimension of below object, and state whether or not it is a fractal. In measuring the volume of the object, when you reduce the length of your ruler by a factor of $5$, the number of volume elements increases by a factor of $125$.

Explain whether the following argument is deductive or inductive. If the sum of the digits of a natural number is divisible by $9$, then the number itself is divisible by $9$. The sum of the digits 279 is $18$, which is divisible by $9$, so we can conclude that $279$ is divisible by $9$.

A $5$-year property costing $\$ 286,000$ is placed in service at midyear in $2011$. The property is depreciated using MACRS. Prepare a depreciation schedule for the property.

If you write out the first several prime numbers $(2,3,5,7,11,13,17,19,23, \ldots)$ you will see that occasionally the gap between two consecutive primes is 2 (for example, $5$, $7$ and $17$,$19$ ). These pairs of closely spaced primes are called twin primes. A famous conjecture states that the number of twin primes is infinite. While a deductive proof of this conjecture has never been found, twin primes with nearly 400,000 digits have been identified, which gives experimental support to the conjecture. Find the first ten pairs of twin primes and present an inductive proof for the truth of the conjecture. Do you think the conjecture is true? Why or why not?

Use a graphing calculator as necessary to explore the graphs of the indicated cross sections.

Let $f(x,y)=4-\sqrt{x^{2}+y^{2}}$.

(A) Explain why $f(a,b)=f(c,d)$ whenever (a,b) and (c,d) are points on the same circle center at the origin in the $xy$ plane.

(B) Describe the cross sections of the surface $z=f(x,y)$ produced by cutting it with the planes $x=0,y=0,$ and $x=y$.

(C ) Describe the surface $z=f(x,y)$.

Explain why the contrapositive is called the inverse of the converse. Is the contrapositive also the converse of the inverse? IN YOUR WORLD

Calculate the correct change for each purchase using the "counting up" method. Write $\textrm{PAY}$ and $\textrm{SAY}$ columns to describe the change given.

$$\begin{aligned} \begin{array}{lll} \textbf{Purchase} & \textbf{ Amount Paid}\\ \$8.63 & \$10.00\\ \end{array} \end{aligned}$$

Use a graphing calculator as necessary to explore the graphs of the indicated cross sections.

Let $f(x,y)=100+10x+25y-x^{2}-5y^{2}$.

(A) Describe the cross sections of the surface $z=f(x,y)$ produced by cutting it with the planes $y=0,y=1,y=2,$ and $y=3$.

(B) Describe the cross sections of the surface in the planes $x=0,x=1,x=2,$ and $x=3$.

(C ) Describe the surface $z=f(x,y)$.

Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. My professor asked me to draw a Venn diagram for a categorical proposition, but I couldn't do it because the proposition was clearly false.