だいがくせいのせんこう is wrong, it means “university student’s major”. I mean, of course one can understand the meaning but it is not correct. You could say: だいがくせいです。せんこうは英語です. Easier and correct. Also, as it’s clear you are talking about you, drop the 私は.
You can also use で to chain your two ideas together:
だいがくせいでせんこうはえいです
There is no mistake, but it is better to use “だいがくせい で” rather than “だいがくせい の”.
The connection between “だいがくせいの” and “せんこう” is not good.
わたしの だいがくの せんこうは えいごです
わたしは だいがくせいで せんこうは えいごです
Minor point but “Joe” would usually be written in katakana, not hiragana.
ジョー* I would change it to.
The second sentence reads as gibberish and the other corrections are spot on.
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だいがくせいのせんこう is wrong, it means “university student’s major”. I mean, of course one can understand the meaning but it is not correct.
You could say: だいがくせいです。せんこうは英語です.
Easier and correct. Also, as it’s clear you are talking about you, drop the 私は.
You can also use で to chain your two ideas together:
だいがくせいでせんこうはえいです
There is no mistake, but it is better to use “だいがくせい で” rather than “だいがくせい の”.
The connection between “だいがくせいの” and “せんこう” is not good.
わたしの だいがくの せんこうは えいごです
わたしは だいがくせいで せんこうは えいごです
Minor point but “Joe” would usually be written in katakana, not hiragana.
ジョー* I would change it to.
The second sentence reads as gibberish and the other corrections are spot on.