A mathematical proposition is an assembly of symbols and letters formed by following certain rules, with the help of logical connectors.
In the calculation of propositions, the propositions used may not have a particular meaning. We can replace a proposition by “Peter is mortal” or “Peter is a man“, for example, and what interests the mathematician is the way that the basic propositions are then combined to construct reasoning.
The expression “inverse proposition” is the name given to the conditional Q → P in opposition to the proposition P → Q.
Mathematical logic dictates that all statements that do not contain a variable can only have one truth value: the statement is either true or false. It cannot be both true and false at the same time (principle of non-contradiction) and it cannot be neither true nor false (principle of excluded middle).