Neither sentence is clear or true. Dogs, cats and mountains are examples of matter. (Not solids) Solid is one of the fundamental states of matter. Examples of solids are iron bars, windows and skeletons. H2O molecules can exist in three states of matter: solid (ice), liquid (water), and gas (steam). We need to determine if the substance is solid, liquid, or gas. (This is ambiguous. Normally it might mean that we expect it to be one of the three and we are identifying which one, but in a different context we might be interested in knowing that it isn’t in the fourth fundamental state, plasma.)

You should use "or" in this sentence: "Solid is a form of matter. It can be a dog, a cat, or a mountain."

"Or". Liquid, solid, and gas are states, not forms of matter.

I think with this sentence 'or' is the way to go. The first sentence (with 'and') sounds that it could be those 3 things simultaneously.