o 'take someone up on something' means to avail of or accept an offer. You can tell someone you would like to take them up on their offer to help you for example or take them up on an invitation. To take someone up on something can also mean to ask someone to explain something or discuss something they have said or done in order to make themselves more clear or because you found what they said strange or you didn't understand. So for example, if someone says something unusual in a meeting or something that doesn't sound correct you can say, "I'd like to take you up on that point because that information doesn't sound correct to me."

1. When I visited Dublin, I took my Irish friend up on his invitation to show me around the city. We had a great time!
2. I always take it up with someone when they make sexist comments. I don't think people should think like that in today's society.

1. After thinking things over for a couple of days, I rang the company to let them know that I would be taking them up on their job offer.
2. I said that I would stay late to complete the work, but in the end, my boss did not take me up on it.
3. I have to take you up on what you have just said. I find that remark very offensive.
4. John took me up on the numbers I quoted last week. He was right to do so, I found some errors in our data.
5. If you have a complaint, you can take it up with management.