Conditionals

Logicals

MATLAB has a class (data type) logical. Logical variables are scalars or arrays of logical 1s and 0s, representing true and false, respectively (in fact, there are “shorthand” variables defined, by default, true and false).

Boolean logic expressions evaluate to either true or false.

Relational operators

Logicals are returned when an expression containing a relational operator is evaluated. Here are MATLAB’s relational operators:

• less than: <,
• greater than: >,
• less than or equal to: <=,
• greater than or equal to: >=,
• equal to: ==, and
• not equal to: ~=.

Exercises

Exercise 1: comparing expressions

Write a script that considers the following statements and returns logical expressions, which should be displayed using the disp command. Assign each logical result to a variable.

• Is 44^2 equal to 1936?
• Is 4^6 greater than or equal to 6^4?
• Is 5^4 less than 5*9*6?

After running your script, you should have a column of logical 0s and 1s.

Exercise 2: exploring the logical class

Run the script from Exercise 1. The Workspace should have the variables to which you assigned the logicals. In the command window, query the data type of one or more of these. Which Class is displayed? I know.

Introducing boolean logic and algebra

Boolean logic and boolean algebra deal with the following five basic logical operations: $\land$ (and), $\lor$ (or), $\neg$ (not), $\implies$ (if…then…), and $\iff$ (if and only if). All but the last of these can be expressed in most programming languages.

The operators and, or, and not

The $\land$, $\lor$, and $\neg$ operators are expressed in MATLAB in the following manners:

• the $\land$ (and) operator is &, &&, or and(expression_1,expression_2);
• the $\lor$ (or) operator is |, ||, or or(expression_1,expression_2); and
• the $\neg$ (not) operator is ~ or not(expression).

The single and and or operators & and | compare element-wise, whereas the double and and or operators && and || assume you are comparing scalar logicals, and are therefore more efficient to use in these cases.

Exercises

Write a script that answers the following questions.

• Is it true that both $37>3^3$ and $\sqrt{9}=4$?
• Is it true that either $37 > 3^3$ or $\sqrt{9} = 4$?
• Is it true that both $8^6 \ne 6^8$ and $4^3 = \sqrt{1844}$?

The operator if, then, etc.

Procedural logic can be expressed in programs with the if conditional statement. The structure of these statements is as follows.

if LOGICAL-EXPRESSION
  STATEMENTS
elseif LOGICAL-EXPRESSION
  STATEMENTS
else
  STATEMENTS
end

The statements under each if and elseif (of which there can be multiple), are only evaluated if the corresponding logical expression returns true. Otherwise, the statements are skipped. If no if or elseif logical expressions evaluate to true, the else statements are evaluated.

It is not necessary to include the elseif and else statements. For instance, it is perfectly valid to do the following.

x = rand(1);
if x > 0.5
  disp('glass is more than half-full, dude')
end

A transgressive exercise

Apparently, we like to gamble. Let’s play. Write a script that generates three random integers between 1 and 3, let’s call them x1, x2, and x3. If none of them are equal—game over. If two of them are equal, we are allowed to try again (re-run the program). If all of them are equal, we win the game.