Some base knowledges

Table value of negation, conjunction, disjunction, exclusive or, conditional, biconditional is too easy to understand, right? 🤪

De Morgan Laws

$$ ⁍ $$

$$ \neg(P\lor Q) = \neg P\wedge \neg Q $$

Distributive Laws

$$ p\wedge(q\lor r)=(p\wedge q) \lor (p \wedge r) $$

Precendence (độ ưu tiên)

1. In parentheses from inner to outer
2. $\neg$
3. $\wedge$
4. $\lor$
5. $\to$

Predicates vs. Quantifiers

Given an example, "For all x's values which are lower than zero, square of them are always positive". In an equation, it will be:

$$ \forall x<0, P(x)=x^2>0 $$

• The red one: is quantifier
• The blue one: is predicate

Logical Equiv