- #1

Ryanodie

- 7

- 0

## 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).