Q: Does "check" have the same meaning in the following two sentences?

Katie's sick, so I need to check up on her and see if she needs anything.

Check whether this page has a watermark.

OPTIONS:
- different meanings
- the same meaning

A: the same meaning

Q: Does "say" have the same meaning in the following two sentences?

Let's say you had a lot of money -- what would you do?

Let us say that he did not tell the truth.

OPTIONS:
- different meanings
- the same meaning

A: the same meaning

Q: Does "know" have the same meaning in the following two sentences?

She doesn't know this composer.

I know him under a different name.

OPTIONS:
- different meanings
- the same meaning

A:
the same meaning