it this sentance correct?

To play football instead of table tennis 這句全部是 noun 是沒問題的，但要留意的是這並非 SVO 句（因為没有 subject - 是誰在 play football？），而是一句 phrase。

在文法上，你第一句是没錯的（除了中間的 full stop 要變成 comma 外）。

在英文中，如果我們想說「為了做 A，我們做 B」，我們可以寫成 To do A, we do B，注意 To do A 這部分不是SVO句，就如剛才 To play football instead of table tennis 那句一樣，無 subject，但後面 we do B 這部分是句SVO句，有subject。

例句: 為了在考試取得佳績，我們努力讀書。
To get good results in the exam, we study hard.

因此，你 To play football instead of table tennis, we can do so to train our legs. 這句是因果倒轉了，你可改成

To train our legs, we play football instead of table tennis.
(為了鍛煉雙腿，我們踢足球而不打乒乓球。）

當然也有其他改法:
We can train our legs by playing football instead of table tennis. (運用了participle)
(我們能以踢足球代替乒乓球來鍛鍊雙腿。)

你也可用we can do so來代替we can train our legs，如果讀者很清楚你在指train our legs。意思是跟剛才那句一樣沒變。

希望幫到你，雖然寫到1999咁。

2013-05-28 02:52:13 補充：
註： we can do so 在 To train our legs, we play football instead of table tennis 這句中是多餘的，因為 To train our legs 已表達了 we can do so 的意思，所以不用包括 we can do so

To play football instead of table tennis. We can do so to train our legs.
當然是有問題，但若改成
To play football instead of table tennis, We can do so to train our legs.
那就沒有問題了

若在To play football instead of table tennis加上句號(full stop)，那表示句子已完成，但這時整句都沒有動詞，所以真是有問題。

但To play football instead of table tennis之後加上逗號(comma)，則表示句子還沒完結。
你或許會問To play football instead of table tennis縱然是加上逗號，這句也沒有動詞不成問題嗎？

這時候To play football instead of table tennis只不過是副詞片語（整句片語只作副詞看待），因此，也無需動詞。

如：In order to get out of the country, you mush have a passport.
To be effective, a poem must be beautiful.

希望幫到你！

To play football instead of table tennis.+ We can do so to train our legs.
= We can play football instead of table tennis to train our legs.

---To play football instead of table tennis will lost the reigning champion
=the person who is champion now
=in mainland China of the world.

To play football instead of table tennis. We can do so to train our legs.

To play football instead of table tennis.
To play is a verbal phrase, while instead of is a prepositional phrase. In this case, there should be a verb or predicate. Therefore to complete this sentence, it is necessary to rewrite as: To play football will train our legs better than that of table tennis.