# Thread: just a few simple questions on set

1. ## just a few simple questions on set

Let S={1,2,3}. Then ⊆ S. Why is this true?

⊆{}. Why is this true?

The set {x∈ : 2x2 - 7x- 4 =0}. How come this one has 2 elements instead of 1?

Thanks.

2. ## Re: just a few simple questions on set

Originally Posted by naturebuilder
Let S={1,2,3}. Then ⊆ S. Why is this true?
⊆{}. Why is this true?
The statement that $A\subseteq B$ means that $\text{if }x\in A\text{ then }x\in B~.$
So for any set $X$ it is true that $\emptyset\subseteq X$