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🚧 Mid of 6.2

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tomit4 2026-07-20 18:56:05 -07:00
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chapter_6/exercises.md
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chapter_6/test_yourself.md
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1. To prove that a set $X$ is a subset of a set $A \cap B$, you suppose that $x$
is any element of $X$ and you show that $x \in A$ _____ $x \in B$.
and
2. To prove that a set $X$ is a subset of a set $A \cup B$, you suppose that $x$
is any element of $X$ and you show that $x \in A$ _____ $x \in B$.
or
3. To prove that a set $A \cup B$ is a subset of a set $X$, you start with any
element $x$ in $A \cup B$ and consider the two cases _____ and _____. You
then show that in either case _____.
$x \in A$; $x \in B$; $x \in X$
4. To prove that a set $A \cap B$ is a subset of $X$, you suppose that _____ and
you show that _____.
$x \in A \cap B$; $x \in X$
5. To prove that a set $X$ equals a set $Y$, you prove that _____ and that
_____.
$X \subseteq Y$; $Y \subseteq X$
6. To prove that a set $X$ does not equal a set $Y$, you need to find an element
that is in _____ and not _____ or that is in _____ and not _____.
$X$; in $Y$; $Y$; in $X$