Sentential calculus is the foundation for discrete and computational mathematics. It teaches you what is logical in a mathematical sense. Let’s begin with some terms.
Every predicate must either equal true or false. Always. There is no null, like it should not exist for booleans.
The sentential connectives connect two or more predicates as mentioned above. Let’s say we have the example
If we want to say x is between 2 and 10 you can do it with the AND connector. But more in this table.
|A=>B||if(!A||B), if(a) then b=true|
In this table I tried to match the connectives with a matchin programming pattern. Of course it’s only pseudo code.
A couple of rules regarding equal predicates:
The de morgan rules are actually pretty simple:
Every time you negate a sentential connective, you negate every predicate and change the connective sign.
Quantifiers give you the ability to generate a predicate from other (multiple) predicates. Let’s say we have two predicates:
Here’s a simpe list of quantifiers using natural numbers: