Four Categorical Statements

Hi, a long time ago a student teacher in my math class wanted to teach a lesson to my class and he decided to teach us the basics of "Logic". I guess it's not logic as in, "Oh, you're suppose to open the peel before you eat the banana." But more sophisticated if you think of it that way. This is just the very basics, I just kinda thought it was cool. So, there are actually FOUR kinds of statements in this whole entire worlds.

Universal Affirmative: A These statements are in the form of All S are P. For example, all squares are shapes that have four sides.

Universal Negative: E These statements are in the form of No S are P. For example, no triangles are shapes that have four sides.

Particular Affirmative: I These statements are in the form of Some S are P. For example, some quadrilaterals are shapes that have equal sides.

Particular Negative: O These statements are in the form of Some S are not P or Not all S are P. For example, some quadrilaterals are not shapes with right angles or not all quadrilaterals are not shapes with right angles.

Wording seem kinda confusing? The easiest way to visualize these statements are using Venn diagrams. The image below (hopefully working, if not link ) shows ways to think about these statements. The shaded area means that there are no members in that group and the "x" means that there are at least one member in that group.

I know, seems kinda useless. However, a fun thing to do with these statements is to transform sentences. Let's say we have a sentence of Ever dog has his day. We can change that sentence into an universal affirmative statement which is All dogs are things that have their day. The key to changing sentences to these statements is to use the phrase "are things" as the predicate. Let's say we have another sentence of No people can breathe fire. Changing that into an universal negative, we say No people are things that can breathe fire. Now you try! Try to change the sentence "A rose by any other name would be as sweet" into one of these statements!

Still not amused. Well, not only that, we can see if a series of statements is viable. I won't rly talk about it in here, but here are some tips:

Try to use Venn diagrams and colour or put x into appropriate parts
Convert the sentences into categorical statements
Make a Venn diagram for the statement you want to prove, and for the statements you are using to prove. See if Venn diagram shows enough information. If it does, then it is true

Okay, so if you got plenty of time, try to see if these statements are true or false:

Some businesses succeed by cutting labor costs. Any business that cuts labor costs is exploiting its workers. Therefore, some businesses exploit their workers.

(Hey, it's just a thing I found, I don't know about business.)

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Four Categorical Statements

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