We can create new propositions by combining existing ones, forming what we call compound propositions. This process is like putting together puzzle pieces represented by letters such as p, q, r, and s. There are three main ways to combine propositions: using “and” (conjunction), “or” (disjunction), and “not” (negation). For instance, let’s consider the propositions:
- p: It’s raining today
- q: Students are excused from school
We can then form compound propositions like:
- p ∧ q: It’s raining today and students are excused from school
- p ∨ q: It’s raining today or students are excused from school
- !p: It’s not raining today / Today is not rainy”