H0: ECE Format

Time Estimate15-30 minutes   Grade Impact1%   DueSep 2 @ 12pm  

Objective
Demonstrate an understanding of the ECE format while building critical thinking skills.

Additional Materials & Formats
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Against my better judgment, I feel the need to prepare you for future courses, which will require you to submit your homework in the ECE Format. This format was designed to simplify grading, something which I believe is a huge disservice and an indicator of a massive flaw in the way we look at education. Nonetheless, the powers that be require me to check a box, so this assignment checks that box.

I figure at the very least, we can use this opportunity for some real learning. The questions in this assignment are largely intended to improve your critical thinking skills, and I encourage you to give every question an honest effort.

The ECE Format

The following document (view PDF) describes the ECE format. Assignments should be completed on engineering paper (available at the large monopolizing online retailer of your choice), but I don’t care if you just use letter or graph paper for this assignment.

Problems

Answer the following questions in the ECE format. Scan and upload your work to Canvas. Questions marked with an * are not evaluated for correctness; every sincere attempt gets full points on these questions.

1. You are confronted with two gates. One gate leads to freedom, and the other to certain doom. At each gate, there is a guard. One of the guards always tells the truth, and the other always lies. You do not know which guard is which. You are allowed to ask one guard a single yes-or-no question to determine which gate leads to freedom. What question would you ask, and why?¹ *

2. You are in a room with three switches. In an adjacent room, there is a single incandescent light bulb. Exactly one switch controls the light bulb. The bulb is initially off, and you cannot see into the adjacent room. You may flip the switches as many times as you like, but you can only enter the adjacent room once. How would you determine which switch controls the light bulb? *

3. Consider the following argument: “All A are B. Some B are C. Therefore, some A are C.” Is this argument valid? Explain your reasoning.

4. Consider the following argument: “If A holds, then B must hold. B holds. Therefore, A holds.” Is this argument valid? Explain your reasoning.

5. Consider the following argument: “All A are B. Some B are not C. Therefore, some A are not C.” Is this argument valid? Explain your reasoning.

6. Consider the following argument: “No A are B. All C are A. Therefore, no C are B.” Is this argument valid? Explain your reasoning.

7. Consider the following “proof” that $1 = 2$. Where is the fallacy in this proof? Explain your reasoning. *

   1. Let $a = b$.
   2. Multiply both sides by $a$: $a^2 = ab$.
   3. Subtract $b^2$ from both sides: $a^2 - b^2 = ab - b^2$.
   4. Factor both sides: $(a - b)(a + b) = b(a - b)$.
   5. Divide both sides by $(a - b)$: $a + b = b$.
   6. Since $a = b$, substitute $b$ for $a$: $b + b = b$.
   7. Simplify: $2b = b$.
   8. Divide both sides by $b$: $2 = 1$.

8. In an alien civilization, everyone has 7 total fingers. How do you think these aliens would represent the numbers 0 through 20? Explain your reasoning. *

9. Consider the following scenario: You are given a black box with two inputs and one output. The box implements a logical operation, but you don’t know which one. Describe a systematic approach to determine the operation performed by the black box. *

10. Pick an object from the list below. Set a 3-minute timer. While the timer runs, list as many uses as you can for that object. *

    • Stapler
    • Brick
    • Soccer ball
    • Dictionary
    • Tissue box
    • Band-aid