I'm all for giving our pets human position food but giving them table scraps has it's problems. Firstly carrots are fine but not so much on the potatoes. You've probably added some generous of seasoning to the food and that would not be great for them either.
By eating the carbs which they need much smaller quantity of in their diets than we do, it will make them too full to eat their hopefully hanging higher protein prepared food at mealtime.
I don't know roughly speaking dogs, but cats *could* eat them so long as they aren't seasoned. But they will be empty calories for them. They'll have food within their bellies but they won't gain any nutrition from it. It would be like us having Snickers for supper.
And if they're uncommon to eating it it might cause a digestive upset.
Answers: Yes, thats biddable for them, if they like them. Watch the potatoes though because they are full of carbs. They are fine in moderation a short time ago like with people :) The individual veggies I would caution you about are the gassy ones like cabbage and broccoli. Also onion is poison to dogs and I assume garlic is too. The vet recommended mini carrot sticks instead of dog bones for my moms overweight dog. she loves them and has lost weight!
Cats are carnivores ie meat eaters. You can feed meat table scraps.
carbs can injure a cat ie potatoes, rice pasta, vegetables offer nothing to a cat but may not do harm
Yes - tons pets like the cooked veggies. However, cats tend to be a little picky and your cat may not eat adjectives of it. Our lab will eat any veggie but lettuce or celery. The cats will nibble on cooked carrots and my one cat like fruit more then veggies.