deletions | additions       diff --git a/q3.tex b/q3.tex  index f8c4111..064b9fa 100644  --- a/q3.tex  +++ b/q3.tex 
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$\sum\nolimits_{u \in A, (u,v) \in E}w_{u,v} >= \frac{1}{2}\sum\nolimits_{u:(u,v) \in E}w_{u,v}$  Similarly, for any $v^' \in A$:  $\sum\nolimits_{u \in B, (u,v^') \in E}w_{u,v^'} >= \frac{1}{2}\sum\nolimits_{u:(u,v^') \in E}w_{u,v}$  Summing over all vertices, we obtain the desired result:  $2c(B) = 2\sum\nolimits_{u \in B,v \in A, (u,v) \in E}w_{u,v} >=sum\nolimits_{e \in E}w_e >= OPT $