English words get used in a variety of ways. For example: the word "but" has slightly different meanings in each of: "all but one", "but that is not true", "it never rains but it pours", "I am old, but you are young". So, if you decide to translate "but" into a single mathematical symbol you will soon run into difficulties. This is even more likely with the words "and" and "or".
That said, sometimes the following translation works:
but ........ ⋀
hence ... ( three dots forming a triangle, this is not available as a character here)
so ...... ( three dots forming a triangle, this is not available as a character here)
Also, the symbols ├ and → and => may sometimes be appropriate for hence or so.