# just a few simple questions on set

• September 20th 2011, 12:30 AM
naturebuilder
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.
• September 20th 2011, 02:42 AM
Plato
Re: just a few simple questions on set
Quote:

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 $\emptyset\subseteq X$