The braces ensure that the to component is properly interpreted. If no from or to component is specified, they are not printed. You can use the keywords union and inter for the union and intersect of sets. This produces large braces, and parentheses are required to surround the terms. You can nest these, of course, with geqn adjusting the sizes properly.
Braces are usually bigger than brackets and parentheses.
For floor and ceiling characters, use the left floor, right floor, left ceiling, and right ceiling commands. To create a pile of elements, use the reserved word pile. This produces output with the three elements a, b, and c stacked vertically within big braces. To make a matrix requires a little more work. You could probably make a matrix using the pile command, but if the elements are not of equal height, they will not line up.