What are three common operators for Boolean searching?

Answer 1

Mathematical operators like +, -, /, * are used with variables to form algebraic expressions, like, a + b - c*d.
NOT, AND and OR are logical operators used to form logical expressions, such as, NOT French, English AND German, English OR German.
NOT operator
Not French - the only specification is that the person should not be French.
The Venn diagram below shows X as the set of French persons, the rest of the area, leaving X, represents those other than French, i.e. X. Thus, the bar negates X, or stands for the complement of X.

X

_

X

0

1

1

0

Truth Table for NOT operator
NOT operates on a single variable hence is a unary operator.

The AND operator

English AND German - our search is narrowed, as we can consider only those who know English as well as German. The logical AND operator is represented by '.' and is called logical multiplication. The Venn diagram shows the rectangle as all the available people, F is English speakers, H is German speakers and the overlapping part is people who know both. AND allows us to pick up only from the overlapped part.

X

Y

X . Y

0

0

0

0

1

0

1

0

0

1

1

1

Truth Table for AND operator
The truth table shows that if X and Y both, are 1, the result of X.Y is 1.


The OR operator

English OR German - our search is broadened, as we can consider people who know English, those who know German, or both. The logical OR operator is represented by '+' and is called logical addition. The Venn diagram shows the rectangle as all the available people, F is English speakers, H is German speakers and the overlapping part is people who know both. OR allows us to pick up from any of the areas covered by F and H.

Truth Table for OR operator

X

Y

X + Y

0

0

0

0

1

1

1

0

1

1

1

1

The truth table shows that if X or Y is 1, the result of X + Y is 1.