Class Review: Conditional Statements, Open Sentences Continued (Kind of)

So I’ve already painstakingly articulated A LOT about conditional statements, which we went over in class today. So instead of outlining my notes again, I thought I’d focus on one thing I was confused about in class that I want to make sure I get right: The difference between being an element and being a subset. The example that confused me a little was:

S ⊆ ℤ (where S is a variable set)

The truth set would have to be comprised of sets itself, NOT just integers. An integer is an element of the set that is a subset of all integers. The proper way to explain the truth set for this open sentence would be {all sets of integers}, NOT {all integers}. Integers are elements, sets of integers are a subset to all integers.

Make sense? Think so.


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