Conjunction term

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A conjunction term (also called a monomial ) is a Boolean function that is formed exclusively by conjunctively linking literals (i.e., all literals are connected by a logical and ). Their general form looks like this:

${\displaystyle \chi _{1}\wedge ...\wedge \chi _{i}\wedge ...\wedge \chi _{n}}$, in which ${\displaystyle \chi _{i}\in \{X_{i},{\overline {X}}_{i}\}}$

A conjunction term which contains all n indices of the Boolean function F: B ⁿ → B¹ under consideration is also referred to as a minterm . The corresponding disjunctive connection is called the disjunction term .

Shortening and expansion

Conjunction terms can be shortened (merged) and expanded (developed). The merging of two conjunction terms can take place if they differ by exactly one literal. This literal occurs normally in one conjunction term and negated in the other. The following example demonstrates the merging. The two conjunction terms

${\displaystyle M_{1}=X_{1}X_{2}{\overline {X_{3}}}X_{4},M_{2}=X_{1}X_{2}X_{3}X_{4}}$

differ in the third place. In the disjunction of these two terms, the third digit can be omitted:

${\displaystyle M_{1}\vee M_{2}=X_{1}X_{2}X_{4}}$

This possibility arises generally from the relationship . The reverse of this relationship is known as expansion or development. By means of repeated developments, minterms can be obtained from conjunction terms. ${\displaystyle AB\vee A{\overline {B}}=A(B\vee {\overline {B}})=A}$

See also

• conjunction