Propositions

What is it?

In Discrete Mathematics, a proposition is a statement that is declared as either true or false. These are given the notation of variables, like $p,q,r,s\dots$ to notate each proposition, e.g. :

• $r=(2+2=5)$
• $p=\text{’Today is going to rain.’}$
• $q=\text{’It rains every single thursday.’}$

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The use of Logical Operators enables complex logic between different propositions, creating other propositions from a preexisting one. Given the implication $p\to q$, other three related implications can be defined:

• Converse

  Defined as $q\to p$.

• Inverse

  Defined as $\neg p\to \neg q$.

• Contrapositive

  Defined as $\neg q\to \bar{p}$.