Logic Operations

I think the most one knows something about logic operations, but let's do a little review.

Logic operations are used for analysis of situations like:

• 2 is bigger than 3? - false
• the vector [1 2 3 4] is larger than [1 3 5]? - true
• the word 'horse' is smaller than 'dog'? - false

The logic operations combine two or more situations, for example:

I'm 22, my father's 52 and my sister's 19.

The question: who is the older?

The solution:

• if I'm older than my father and my sister then I'm the older.
• if my father's older than me and my sister then he's the older.
• if my sister's older than my father and me then she's the older.

The and is a logic operator.

The logic operators are used with logic variables. Logic variables are like numeric variables but the values are true or false.

The basic logic operators are: {not, or, and}

The not is a unary operator and the others are binary operators.

So, follow the possible logic situations for each operation:

NOT

• not(true) is false
• not(false) is true

AND

• false and false is false
• false and true is false
• true and false is false
• true and true is true

OR

• false or false is false
• false or true is true
• true or false is true
• true or true is true

A mental train.

If I want a racket and a ball but I have just a racket I'm not satisfied. But, If I want a ball of basketball or a ball of soccer, so I need one ball or both.


The Scilab has that three operators.

The operator '~' is the not.

The operator '|' is the or.

The operator '&' is the and.

The operations or and and can be applied on vectors with the functions or(.) and and(.).

Let's play now.

-->x = 10;

-->y = 15;

-->z = x + y
z =

25.

-->(x > y) & (z > x) // x is smaller than y then the first operation is false
ans =

F

-->(x > y) | (z > x) // z is bigger than x then the second operation is true
ans =

T

-->~((x > y) & (z > x)) // the result is the inverse of the first result
ans =

T

-->~((x > y) | (z > x)) // the result is the inverse of the second result
ans =

F


The results are F (false) or T (true) because logic operations give logic results.

If you want use the variables with logic values:

-->r1 = %F
r1 =

F

-->r2 = %T
r2 =

T

-->and([r1 r2])
ans =

F

-->or([r1 r2])
ans =

T


For finish the post, if you use a numeric variable with logic operators, thus the Scilab interprets the 0 (zero) as false and different of 0 (zero) as true.

-->x = 0;

-->y = 2;

-->z = -5;

-->x | y | z
ans =

T

-->x & y & z
ans =

F

-->x & z
ans =

F

-->x & y
ans =

F

-->y & z
ans =

T