We now have two sentence-operators in our formal language: ampersand (‘&’) and tilde (‘~’). This highlights the possibility of having sentences which contain two sentence operators.
(That possibility was present already: for instance, we could have had something equivalent to ‘It’s raining and it’s cold and it’s windy’.)
Sentences with two or more operators are common in natural languages. For example
It’s warm and it’s not raining
We could represent this in our formal language. First we create our dictionary: