A discrete mathematics problem by ashwin korade

Discrete Mathematics Level 3

A shop sells two kinds of rolls- egg roll and mutton roll. Onion, tomato, carrot, chili sauce and tomato sauce are the additional ingredients. You can have any combination of additional ingredients, or have standard rolls without any additional ingredients subject to the following constraints:

(a) You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.
(b) If you have onion or tomato or both you can have chilli sauce, but not otherwise.

How many different rolls can be ordered according to these rules?


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