Create two vectors.

X = [1 0 0 1 1];
Y = [0 0 0 0 0];

Using the short-circuit OR operator with X and Y returns an error. The short-circuit operators operate only with scalar logical conditions.

Use the any and all functions to reduce each vector to a single logical condition.

any(X) || all(Y)

ans = logical
   1

The expression is equivalent to 1 OR 0, so it evaluates to logical 1 (true) after computing only the first condition, any(X).

Specify a logical statement where the second condition depends on the first. In the following statement, it doesn't make sense to evaluate the relation on the right if the divisor, b, is zero.

b = 1;
a = 20;
x = (b ~= 0) && (a/b > 18.5)

x = logical
   1

The result is logical 1 (true). However, if (b ~= 0) evaluates to false, MATLAB® assumes the entire expression to be false and terminates its evaluation of the expression early.

Specify b = 0 and evaluate the same expression.

b = 0;
x = (b ~= 0) && (a/b > 18.5)

x = logical
   0

The result is logical 0 (false). The first statement evaluates to logical 0 (false), so the expression short-circuits.

Create a structure with fields named 'File' and 'Format'.

S = struct('File',{'myGraph'},'Format',[])

S = struct with fields:
      File: 'myGraph'
    Format: []

Short-circuit expressions are useful in if statements when you want multiple conditions to be true. The conditions can build on one another in such a way that it only makes sense to evaluate the second expression if the first expression is true.

Specify an if statement that executes only when S contains an empty field named 'Format'.

if isfield(S,'Format') && isempty(S.Format)
  S.Format = '.png';
end 
S

S = struct with fields:
      File: 'myGraph'
    Format: '.png'

The first condition tests if 'Format' is the name of a field in structure S. The second statement then tests whether the Format field is empty. The truth of the second condition depends on the first. The second condition can never be true if the first condition is not true. Since S has an empty field named 'Format', the body statement executes and assigns S.Format the value '.png'.