- #1

- 57

- 1

There are four statements and I need to explain why they are true. (they all are)

I understand it why some of they are, but my answers just don't feel accurate/formal enough.

## Homework Equations

1) [itex]\mathbb{R}^3 \subseteq \mathbb{R}^3[/itex]

2) [itex]\mathbb{R}^2 \nsubseteq \mathbb{R}^3[/itex]

3) [itex]\left \{ (x,y): x - 1= 0 \right \} \subseteq \left \{ (x,y): x^2 - x = 0 \right \} [/itex]

4) [itex]\left \{ (x,y): x^2 - x = 0 \right \} \nsubseteq \left \{ (x,y): x - 1 =0 \right \}[/itex]

## The Attempt at a Solution

1) is true simply because

**X is a subset of X for any set X.**no problem with this one

2) is not so obvious for me.

I understand that one consists of ordered pairs and the other of ordered triples. But I'm not sure if this affects anything.

3) is true because

**{ 1 } is a subset of { -1 , 1}**

4) is true because

**{ -1 , 1 } is not a subset of { 1 }**

By The way: I was having trouble with 3 and 4. But I kinda got an insight while typing.

not sure if it could be more formal maybe.

So the really troubling one is 2.