logic formulas

<2023-05-25 Thu 08:21:55>

math

note that $\text{[math]}$ and $\text{[math]}$ represent true and false, respectively

propositional logic

equivalence

number	equivalence	rule name
E1	$\text{[math]}$
E2	$\text{[math]}$
E3	$\text{[math]}$
E4	$\text{[math]}$
E5	$\text{[math]}$
E6	$\text{[math]}$
E7	$\text{[math]}$
E8	$\text{[math]}$
E9	$\text{[math]}$
E10	$\text{[math]}$
E11	$\text{[math]}$
E12	$\text{[math]}$
E13	$\text{[math]}$
E14	$\text{[math]}$	distributivity
E15	$\text{[math]}$	distributivity
E16	$\text{[math]}$	de morgan
E17	$\text{[math]}$	de morgan
E18	$\text{[math]}$
E19	$\text{[math]}$
E20	$\text{[math]}$
E21	$\text{[math]}$
E22	$\text{[math]}$
E23	$\text{[math]}$

logical implication

number	implication	rule name
I1	$\text{[math]}$
I2	$\text{[math]}$
I3	$\text{[math]}$
I4	$\text{[math]}$
I5	$\text{[math]}$
I6	$\text{[math]}$
I7	$\text{[math]}$
I8	$\text{[math]}$
I9	$\text{[math]}$
I10	$\text{[math]}$
I11	$\text{[math]}$
I12	$\text{[math]}$
I13	$\text{[math]}$
I14	$\text{[math]}$

first-order logic

logical implication

number	implication
I'1	$\text{[math]}$
I'2	$\text{[math]}$
I'3	$\text{[math]}$
I'4	$\text{[math]}$
I'5	$\text{[math]}$
I'6	$\text{[math]}$
I'7	$\text{[math]}$
I'8	$\text{[math]}$
I'9	$\text{[math]}$
I'10	$\text{[math]}$

rule of inference

name	rule of inference
Universal Instantiation	$\text{[math]}$ where $\text{[math]}$ is some arbitrary element of the universe
Universal Generalization	$\text{[math]}$ where $\text{[math]}$ holds for every element $\text{[math]}$ of the universe
Existential Instantiation	$\text{[math]}$ where $\text{[math]}$ is some element of the universe of discourse. it is not arbitrary but must be one for which $\text{[math]}$ is true
Existential Generalization	$\text{[math]}$ where $\text{[math]}$ is an element of the universe

de morgan

$\text{[math]}$