I have used the word dichotomy before. I have never used the phrase "false dichotomy". This is probably because the only time I think of using the word is when...um...I notice a dichotomy. I can't think of a good example off the top of my head so here's a poor example: "The United States is the most affluent society in the world but notice the dichotomy between rich and poor in this country." Often you can use "dichotomy" when you notice differences that are sociological in nature as opposed to, for example, physical differences between things. It's a word that is not that commonly used.

This word usually only appears in the phrase "false dichotomy". I am not sure I have used the word "dichotomy" in any other way than saying "false dichotomy". A false dichotomy means you assume only A and B are true. A simpler synonym is "black and white" . Examples: "To say people are either pro-war or anti-war is a false dichotomy. This is a complicated subject, and people have many different views and opinions." "Things are not so 'black and white'. There is often a 'grey area'. "