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Fix grammar

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Antti H S Laaksonen 2017-04-19 21:31:36 +03:00
parent 9ca906ee77
commit 24407fb106
1 changed files with 2 additions and 2 deletions
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chapter20.tex
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@ -947,7 +947,7 @@ that contains all left nodes exists
exactly when for each $X$, the condition $|X| \le |f(X)|$ holds. exactly when for each $X$, the condition $|X| \le |f(X)|$ holds.
Let us study Hall's theorem in the example graph. Let us study Hall's theorem in the example graph.
First, let $X=\{1,3\}$ and $f(X)=\{5,6,8\}$: First, let $X=\{1,3\}$ which yields $f(X)=\{5,6,8\}$:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.60] \begin{tikzpicture}[scale=0.60]
@ -971,7 +971,7 @@ First, let $X=\{1,3\}$ and $f(X)=\{5,6,8\}$:
The condition of Hall's theorem holds, because The condition of Hall's theorem holds, because
$|X|=2$ and $|f(X)|=3$. $|X|=2$ and $|f(X)|=3$.
Next, let $X=\{2,4\}$ and $f(X)=\{7\}$: Next, let $X=\{2,4\}$ which yields $f(X)=\{7\}$:
\begin{center} \begin{center}
\begin{tikzpicture}[scale=0.60] \begin{tikzpicture}[scale=0.60]