🚧 Midway through 6.1

chapter_6/test_yourself.md

@@ -4,25 +4,51 @@ Page 411$a
 
 1. The notation $A \subseteq B$ is read "_____" and means that _____.
 
+The set $A$ is a subset of the set $B$; if $x \in A$ then $x \in B$
+
 2. To use an element argument for proving that a set $X$ is a subset of a set
    $Y$, you suppose that _____ and show that _____.
 
+$x$ is a particular but arbitrarily chosen element of $X$; $x$ is an element of
+$Y$.
+
 3. To disprove that a set $X$ is a subset of a set $Y$, you show that there is
    _____.
 
+an element in $X$ that is not in $Y$.
+
 4. An element $x$ is in $A \cup B$ if, and only if, _____.
 
+$x$ is in either $A$ or $B$.
+
 5. An element $x$ is in $A \cap B$ if, and only if, _____.
 
+$x$ is in both $A$ and $B$.
+
 6. An element $x$ is in $B - A$ if, and only if, _____.
 
+$x$ is in $B$ but not in $A$.
+
 7. An element $x$ is in $A^c$ if, and only if, _____.
 
+$x$ is in the universal set and is not in $A$.
+
 8. The empty set is a set with _____.
 
+no elements.
+
 9. The power set of a set $A$ is _____.
 
+the set of all subsets of $A$.
+
 10. Sets $A$ and $B$ are disjoint if, and only if, _____.
 
+they have no elements in common, or $A \cap B = \emptyset$.
+
 11. A collection of nonempty sets $A_1, A_2, A_3, \dots$ is a partition of a set
     $A$ if, and only if, _____.
+
+all $A_i$ are a subset of $A$, but are also disjoint.
+
+$A$ is the union of all the sets $A_1, A_2, A_3, \dots$ and
+$A_i \cap A_j = \emptyset$ whenever $i \neq j$.