Given an alphabet $\Sigma = \{0,1\}$. Can you please explain what will be the set in each one of these expressions below:
$$\Sigma \cup \{\epsilon\}\ =\ ?\\ \Sigma \cup \{\emptyset\}\ =\ ?\\ \Sigma \cup\emptyset\ =\ ?$$
This is really confusing me and I could not find answer for this.
Since $A\cup B$ is the set of things which either are in $A$ or they are in $B$, the three sets are respectively $$\{0,1,\epsilon\}\\ \{0,1,\emptyset\}\\ \{0,1\}$$ Though the significance of the second one as a set of strings is rather questionable, to say the least.