Sentences with more than one connective

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:

• W: It’s warm
• R: It’s raining

Then we can construct our sentence:

• (W & ~R)