Proofs with Sets

One of the basic ways of doing a proof with sets is the Element Argument. What is it?

Element Argument: Proof subset-ness

Let sets $X$ and $Y$ be a given. To prove $X\subseteq Y$:

1. Suppose $x$ is a particular but arbitrarily chosen element of $X$,
2. Show that $x$ is an element of $Y$

Proving Sets are Equal:

Basic way of proving sets are equal:

• Prove $X\subseteq Y$
• Prove $Y\subseteq X$

Example: