Logic - 1
This topic is very similar to the subjects covered in COMP111’s propositional logic. As result I will only be noting down significant differences.
Logic is concerned with the truth a falsity of statements. The question is when does a statement follow from a set of statements.
Propositional Logic
Propositional logic is logic which only concerns itself with whether something is true or false. Other languages differ themselves as they deal with uncertainties.
A proposition is a statement that can either be true or false. A statement like $4+5$ is not a proposition as it doesn’t give a true or false answer.
Compound Propositions
More complex propositions are formed using logical connectives (also called Boolean connectives).
The basic connectives are:
- $\neg$: Negation (read “not”).
- $\wedge$: Conjunction (read “and”).
- $\vee$: Disjunction (read “or”).
- These are the scientific names and they make a difference between the english and mathematical words.
- $\Rightarrow$: Implication (read “if…then”).
- In other schools this may be written as $\rightarrow$ or as $\subseteq$.
- $\Leftrightarrow$: Equivalence (read “if, and only if,”).
- Similar to 4. the notation is not as set as 1,2 and 3. This may be written as $\leftrightarrow$ or $\equiv$.
Propositional formed using these logical connectives are called compound propositions; otherwise atomic propositions.
- A propositional formula is either an atom ic or compound proposition.