What are appropriate chores for a 10 year old?

I have an 11 yo daughter, and her chores are to do the dishes, help with dinner, set the table, and help dust/vacuum. She wants a cat or a hamster, and I have told her that she cannot have one because she is yet to squeamish to clean up after them, but if she were to have a pet, it would be her responsibility to clean up after it, feed it, etc.

All the things mentioned and anything that reasonable.

I have a 10 year old son. He takes out the trash, sweeps the kitchen floor two nights/week, cleans his bathroom (except the tub/shower and the floors, I do that), does one load of laundry/week (wash, dry and fold), cleans his room, vacuums his room and one other room of my choice, changes his sheets weekly and dusts one room other than his.

By the age of 10 I think they are plenty old enough to do chores around the house. My 4 year old helps set the table and pick up little things around the home. She enjoys helping and I believe that giving children responsibility will help them grow. When my daughter seems me doing things even like cooking and dishes she enjoys grabbing a chair and wanting to help. In my opinion a child should learn to take responsibility and get the satisfaction from doing things and doing them right at a young age. If your children (boy or girl) learn now it will be easier for them later and they wont expect everyone else to take care of them as adults. they will know how. I am thankful now my mother instilled and gave me the responsibilites she did when I was young.

doing dishes, taking the trash out, keeping his room clean, set the table, vacuum

You have to determine what is safe and appropriate based on your knowledge of his personality and abilities, but don't be afraid to give him a chore you think is safe for him to do, even if he doesn't do the best job and you end up having to check on his work. He needs to eventually learn to do everything; someday he will have a household of his own.

My daughter is 11 and has been doing the same chosres four a couple of years. She rotates chores with her sister, so everything listed is not done at the same time. Dishes (loads them into the dishwasher, unloads them and puts them away, wipes off counters with cleaning wipes), upstairs bath (weekly uses cleaning wipes to clean sink, takes out bathroom trash, swipes toliet), laundry (at least one load a day - sort, wash, dry, fold and deliver), trash (takes out kitchen trash, replaces bag and moves dumpster to street on trash day), feed cats, clean litter box, clean her room (has to be touched up daily).

dishes, trash, vacuum, put away laundry, clean his room

Trash, dishes, setting the table, helping with/doing her own laundry.