Introduction and formalization of Boolean algebra

Recently I’ve been teaching my friend boolean algebra for their exams at university. Some exercises included simplifying boolean expressions. While teaching them, I noticed that we mostly relied on the transformation rules and almost mechanically simplified expressions (M of MIU, remember? :))

In this post, we will formalize this algebra and prove some properties about it.

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Wisdom of the crowd exercise

According to Wikipedia, the wisdom of the crowd is the collective opinion of a group of individuals rather than that of a single expert. An explanation for this phenomenon is that there is idiosyncratic noise associated with each individual judgment, and taking the average over a large number of responses will go some way toward canceling the effect of this noise.

We’ll take the results of a YouTube video as an example, to test the wisdom of the crowd. I used Majk’s Show as a dataset. It’s a young local guy that interviews random people on the streets, asking them random questions.

We will agree that any hits above 50% will validate the wisdom of the crowd. Follows a table with results:

Question Answer Correct answers (%) Valid?
How do you pronounce “schedule” sheh·jool or skeh·jool 13/34 = 38.23% No
Who’s the man on the picture Albert Einstein 14/32 = 43.75% No
8/2(2+2)=? 16 11/25 = 44% No
What’s closer, America or the Moon? America 9/22 = 40.9% No
Who was the first president of Macedonia? Kiro Gligorov 22/50 = 44% No
What is larger: -4 or -10? -4 20/36 = 55.55% Yes

We can further categorize the questions and see where the wisdom of the crowd fails specifically. For example, English seems to be below 40% while everything else is above 40%.

In any case, I think I might have set a bit high grading point for the citizens of my country 🙂 But at least they seem to know how to compare two numbers!