58 lines
1.6 KiB
Markdown
58 lines
1.6 KiB
Markdown
Page 515
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**Test Yourself**
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1. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
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$x R y$ means that ____.
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$x$ is related to $y$ by $R$
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2. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
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$x \cancel{R} y$ means that ____.
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$x$ is not related to $y$ by $R$.
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3. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
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$(y, x) \in R^{-1}$ if, and only if, ____.
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$$ (x, y) \in R $$
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4. A relation on a set $A$ is a relation from ____ to ____.
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$A$; $A$
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5. If $R$ is a relation on a set $A$, the directed graph of $R$ has an arrow
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from $x$ to $y$ if, and only if, ____.
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$x$ is related to $y$ by $R$
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---
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Page 526
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**Test Yourself**
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1. For a relation $R$ on a set $A$ to be reflexive means that ____.
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2. For a relation $R$ on a set $A$ to be symmetric means that ____.
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3. For a relation $R$ on a set $A$ to be transitive means that ____.
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4. To show that a relation $R$ on an infinite set $A$ is reflexive, you suppose
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that ____ and you show that ____.
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5. To show that a relation $R$ on an infinite set $A$ is symmetric, you suppose
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that ____ and you show that ____.
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6. To show that a relation $R$ on an infinite set $A$ is transitive, you suppose
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that ____ and you show that ____.
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7. To show that a relation $R$ on a set $A$ is not reflexive, you ____.
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8. To show that a relation $R$ on a set $A$ is not symmetric, you ____.
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9. To show that a relation $R$ on a set $A$ is not transitive, you ____.
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10. Given a relation $R$ on a set $A$, the transitive closure of $R$ is the
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relation $R^t$ on $A$ that satisfies the following three properties: ____,
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____, and ____.
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