Full disjunction

A full disjunction (also: max term ) is a special disjunction term in propositional logic . H. a number of literals , all linked by a logical or ( ). All variables of the considered -digit Boolean function must appear in the disjunction term in order to be able to speak of a full disjunction. Examples are: ${\displaystyle \vee }$ ${\displaystyle n}$ ${\displaystyle n}$

• ${\displaystyle e_{1}\vee e_{2}}$
• ${\displaystyle e_{1}\vee \neg e_{2}\vee e_{3}}$
• ${\displaystyle \neg e_{1}\vee e_{2}\vee e_{3}}$

Full disjunctions can be combined to form a conjunctive normal form.

Comparison of Minterm / Maxterm

The following table shows the difference between the maxterm and minterm representation :

index	${\displaystyle x_{2}}$ ${\displaystyle x_{1}}$ ${\displaystyle x_{0}}$	Minterm	Max term
0	0 0 0	${\displaystyle \neg x_{2}\wedge \neg x_{1}\wedge \neg x_{0}}$	${\displaystyle x_{2}\vee x_{1}\vee x_{0}}$
1	0 0 1	${\displaystyle \neg x_{2}\wedge \neg x_{1}\wedge x_{0}}$	${\displaystyle x_{2}\vee x_{1}\vee \neg x_{0}}$
2	0 1 0	${\displaystyle \neg x_{2}\wedge x_{1}\wedge \neg x_{0}}$	${\displaystyle x_{2}\vee \neg x_{1}\vee x_{0}}$
3	0 1 1	${\displaystyle \neg x_{2}\wedge x_{1}\wedge x_{0}}$	${\displaystyle x_{2}\vee \neg x_{1}\vee \neg x_{0}}$
4th	1 0 0	${\displaystyle x_{2}\wedge \neg x_{1}\wedge \neg x_{0}}$	${\displaystyle \neg x_{2}\vee x_{1}\vee x_{0}}$
5	1 0 1	${\displaystyle x_{2}\wedge \neg x_{1}\wedge x_{0}}$	${\displaystyle \neg x_{2}\vee x_{1}\vee \neg x_{0}}$
6th	1 1 0	${\displaystyle x_{2}\wedge x_{1}\wedge \neg x_{0}}$	${\displaystyle \neg x_{2}\vee \neg x_{1}\vee x_{0}}$
7th	1 1 1	${\displaystyle x_{2}\wedge x_{1}\wedge x_{0}}$	${\displaystyle \neg x_{2}\vee \neg x_{1}\vee \neg x_{0}}$

Realization of circuits with mintermen / maxterms:

	Minterm	Max term
0	NOR gate	AND gate
1	OR gate	NAND gate

There are also full conjunctions .