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Subsection Joining Two Statements
Many questions involve multiple conditions. For example, to determine if a number is an even number greater than 100, then you need to check two things at once:
Because both must be true, we join these statements with “and”. If either of these conditions could be true, then we would join them with “or”.
MATLAB joins logical statements with AND and OR using the operators
& (AND) and
| (OR).
Table 23. Logical operators for combining statements
\(\textbf{Logical}\) \(\textbf{operator}\)
\(\textbf{Logical statement}\)
\(\textbf{Question being asked}\)
&Are both \(\texttt{ans1}\) and \(\texttt{ans2}\) true?
|ans1 | ans2\(\text{Is at least one of}\ \texttt{ans1}\ \text{or}\ \texttt{ans2}\ \text{true?}\)
The result of joining logical statements are exactly what you would expect from everyday language: AND is true only when both sides are true, while OR is true when at least one side is true.
% Quick checks
true & true % → true: 1 (logical)
true & false % → false: 0 (logical)
false & true % → false: 0 (logical)
false & false % → false: 0 (logical)
true | true % → true: 1 (logical)
true | false % → true: 1 (logical)
false | true % → true: 1 (logical)
false | false % → false: 0 (logical)
Now try these operators in context.
P = 1;
Q = 10;
R = -4;
P <= R & P > Q % → false & false: 0 (logical)
R < 0 & R < Q % → true & true: 1 (logical)
Q == R | Q == P % → false | false: 0 (logical)
P < Q | P < R % → true | false: 1 (logical)
~(P < Q & P < R) % → NOT (true & false): 1 (logical)
P > Q | P > R % → false | true: 1 (logical)
Checkpoint 24 . Combining Logical Statements.
Given
age = 25 and
hasLicense = true, which expression is the
most readable way to ask "Is the person at least 18 years old AND has a driver’s license?"
(age >= 18) & hasLicense
Correct! This is clear and readable, using the AND operator directly with meaningful variable names.
(age >= 18) | hasLicense
Incorrect. The OR operator returns true if either condition is true, but we need both conditions to be true.
age >= 18 & hasLicense == true
While logically correct, comparing hasLicense == true is redundant and less readable. Use hasLicense directly since it’s already a logical value.
~(age < 18 | ~hasLicense)
While logically equivalent (using De Morgan’s Law), this is much harder to read. Prefer the straightforward AND version for clarity.
