- #1
Ryanodie
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Homework Statement
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I am going through Apostol's Calculus volume 1 and am working through I 2.5 #3. I'm not very familiar with doing proofs so I just wanted to make sure that I got the right idea here.
Here's the question:
Let A = {1}, B = {1,2}
Prove:
1. ## A \subset B ##
2. ## A \subseteq B ##
3. ## 1 \in A ##
Homework Equations
Basic set notation
The Attempt at a Solution
1.
A is said to be a proper subset of B if ## x \in A ## is in B and if ##B \ne A##.
## x \in B ##.
## B \ne A ##.
Therefore, A is a proper subset of B.
2.
A is said to be a subset of B if every element ##x \in A## is also in B.
## x \in B ##
Therefore, A is a subset of B.
3.
x is said to be an element of A if ## x \in A ##
x=1
## x \in A ##
Therefore, ## 1 \in A ##
I don't really know how to compose these, so this was my best shot. Let me know if I did alright or if their is a different way to write these (or if it's flat out wrong).