CHARTS & TABLES Boolean Algebra
CHARTS & TABLES Boolean Algebra
Boolean Algebra
This particular type of algebra is based on logic and logical statements, and is used
for sets, diagrams, probability, and computer design and applications. Typically,
statements are represented by letters such as p, q, r,and s.For example:
pis “3 belongs to a set of odd numbers”
qis “2 belongs to the same set of numbers as 3”
ris “ice cream is a dairy product”
sis “chocolate ice cream is the best-selling dairy product”
Statements can be true or false, and they can be combined to form compound
statements. Since compound statements in Boolean algebra follow logic, one
statement can be true, another can be false, and when combined together the
compound statement can be either true or false depending on the conditions placed
on the statement. Let’s use pand qfor our example compound statements:To indicate it is written and it is called a(n)
pand q p^q conjunction
por qpqdisjunction
if p,then q p→q conditional
pif and only if q p↔q equivalence
not pp′ negation
The “truths” of the compound statements are determined by the value of each
statement on its own, and then the combined value. So, in the example of the
conjunction pand q,written p^q,if pis true on its own and qis true on its own, then
the conjunction of pand qis true. But if either por qis false, then the conjunction
statement p^qis false.In a disjunction, however, where the statement is por q,written p∨q,if one of the
statements is true then the compound statement is true, and it is only false if both
statements are false.^