[cab]

You can. Whether its a good idea or not depends on what the veggies are.

Tomatoes, peas and beans are excellent for seed saving. Squashes, courgettes etc. are tarts that cross with any other squashes and courgettes so if you want to save seed you need to be a bit more clever how you do it. Carrots, parsnips and other veg with close wild relatives can be a bit random. Lettuce is easy enough. Brassicas are, again, rather promiscuous so you need to exclude them from other brassica flowers. Beets and relatives are interesting, more often than not you do okay with chard self seeding, but beetroot seems to lose out a little.

[cab]

Cabbage, kale, cauliflower, broccoli, calabrese, and suchlike. They're all basically more or less the same plant; turnip is near as dammit the same plant as rape, so you may struggle to get good home saved turnip seed.

Rocket is also a brassica, and it'll cross with other rockets but what you get is usually still pretty good; generally, I sow rocket once a year, and I let some self seed about the place too, and this approach secures a more or less constant supply. I just weed it out when theres too much of it.

[Slim]

And sometimes even if they say that they are...