Do these two statements mean the same thing
你今天有事儿吗？

and

你今天有空吗

I keep getting tripped up by these because they seem so similar. If they are used interchangeably i I would be so happy because that would mean I could move on to something else.

Question

Do these two statements mean the same thing
你今天有事儿吗？

and

你今天有空吗

I keep getting tripped up by these because they seem so similar. If they are used interchangeably i I would be so happy because that would mean I could move on to something else.

Answer

Though 你今天有事吗=Are you busy, 你今天有空吗=Are you free, they mean the same in Chinese. When you want to know if the person are free you can make the both questions.

Answer

你今天有事儿吗？ = Are you busy?
你今天有空吗？ = Are you free?

So:
1. Yes, they do mean the same.
2. No, they don't mean the same.

Do you get tripped up on the two sentences in English, too?

Answer

Totally,both of them mean the same thing.However,"你今天有事儿吗？"has one other mean,when some body else look wrong, you can care for him with"你今天有事儿吗？"or"你今天发生了什么事？"