🚧 Progress through chapter 1

chapter_1/test_yourself.md

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+**Test Yourself**
+
+Page 28
+
+1. A universal statement asserts that a certain property is _______ for _______.
+
+2. A conditional statement asserts that if one thing _______ then some other
+   thing _______.
+
+3. Given a property that may or may not be true, an existential statement
+   asserts that _______ for which the property is true.
+
+**Solutions**:
+
+1. true, for all elements of a set.
+
+2. is true, also has to be true.
+
+3. there is at least one thing
+
+---
+
+**Test Yourself**
+
+Page 37
+
+1. When the elements of a set are given using the set-roster notation, the order
+   in which they are listed _______.
+
+**Solution**
+
+does not matter.
+
+2. The symbol $\mathbb{R}$ denotes _______.
+
+**Solution**
+
+The set of all real numbers.
+
+3. The symbol $\mathbb{Z}$ denotes _______.
+
+**Solution**
+
+The set of all integers.
+
+4. The symbol $\mathbb{Q}$ denotes _______.
+
+**Solution**
+
+The set of all rational numbers.
+
+5. The notation $\{x | P(x)\}$ is read _______.
+
+**Solution**
+
+The set of all $x$ such that $P(x)$ is true.
+
+6. For a set $A$ to be a subset of a set $B$ means that _______.
+
+**Solution**
+
+Every element in $A$ is an element in $B$.
+
+7. Given sets $A$ and $B$, the Cartesian product $A \times B$ is _______.
+
+**Solution**
+
+The set of all ordered pairs $(a, b)$ where $a \in A$ and $b \in B$.
+
+8. Given sets $A$, $B$, and $C$, the Cartesian product $A \times B \times C$ is
+   _______.
+
+The set of all ordered triples, $(a, b, c)$ where $a \in A$ and $b \in B$ and
+$c \in C$.
+
+**Solution**
+
+9. A string of length $n$ over a set $S$ is an ordered $n$-tuple of elements
+   $S$, written without _______ or _______.
+
+**Solution**
+
+parentheses; commas