Propositional Logic and Operators

As we emphasized previously, a proposition can be either "true" or "false". We can use propositional variables to represent real-life events, such as "it will rain today" or "we will go watch the soccer game today". A complex logic expression will be one that combines one or more simple propositional variables together using the logical operators we've seen on the previous slide.

Example: The proposition:

It won't rain today, and we will go watch the soccer game today.

contains the two simple events "it will rain today" or "we will go watch the soccer game today". However, we first negated the 1st event (so it turned into "it won't rain today") and then ANDed it with the 2nd event.

If we denote $p = \;($"$\text{it will rain today}$"$)$ and $q = \;($"$\text{we will go watch }$$\,\text{the soccer game today}$"$)$, then we can represent our proposition with the expression: $(\neg p) \wedge q = \neg p \wedge q$.