Betti numbers of 3-manifolds (Ex)

Let $G$$<wikitex>;
 Let $G$ be the fundamental group of a closed orientable $-manifold. Show that $b_2(G) \le b_1(G)$. 
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[[Category:Exercises]]
[[Category:Exercises without solution]]G$ be the fundamental group of a closed orientable $3$$3$-manifold. Show that $b_2(G) \le b_1(G)$$b_2(G) \le b_1(G)$. 

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