Exercise 2.1

Question

Exercise 1: Prove that the empty set is a subset of every set.

ghostofgarborg · Accepted Answer

Let $S$ be any set. The empty set $\emptyset$ is a subset of $S$ iff for all $x \in \emptyset$, $x \in S$. 
    This is vacuously true, so we are done.

Amit Awasthi · Answer

\begin{proof}
      To prove $\emptyset \subset A$ for all sets $A$, we have to prove that every element $x \in \emptyset$ is also in $A$ by Definition 1.3. Since there are no points in $\emptyset$ by Definition 1.3, $\emptyset$ is a subset of every set.
\end{proof}

Exercise 2.1

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Exercise 2.1

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