I am worried about his health.
I am concerned about his health.
I worry about his health.
Are all grammatical? (above)
Which one is commonly used?
Would you let me know other similar expressions?
I don't like both of them.
(Is this the following in meaning?)
= I like one of them, but I don't like the other of them.
Among the first three, all are grammatical. The first is probably the most commonly used.
Rather than "I don't like both of them" (uncommon phrasing), you should say, "I don't like either of them." That's when you simply don't like them at all. If you like one but not the other, then you have to say it like that -- "I like this one, but not that."
Yes, all three sentences are grammatical:
1. "I am worried about his health."
2. "I am concerned about his health."
3. "I worry about his health."
The second sentence, "I am concerned about his health," is the most commonly used and is a more formal way of expressing worry or care for someone's well-being. The other two sentences are also fine, but they may sound slightly more informal or casual in comparison.
Regarding your second question, here are a few similar expressions to convey concern for someone's health:
1. "I'm troubled by his health."
2. "I'm disturbed by his health condition."
3. "His health is a source of anxiety for me."
As for your last question, the sentence "I don't like both of them" does not convey the same meaning as your suggested interpretation. "I don't like both of them" actually means that you dislike both options equally. If you want to express that you like one option but not the other, you could say, "I like one of them, but I don't like the other one."