From 24407fb106082532989407159750674d91cb44fd Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Wed, 19 Apr 2017 21:31:36 +0300
Subject: [PATCH] Fix grammar

---
 chapter20.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapter20.tex b/chapter20.tex
index 1e7a8d0..a4a089a 100644
--- a/chapter20.tex
+++ b/chapter20.tex
@@ -947,7 +947,7 @@ that contains all left nodes exists
 exactly when for each $X$, the condition $|X| \le |f(X)|$ holds.
 
 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{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
 $|X|=2$ 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{tikzpicture}[scale=0.60]