Final answer:
The statement is true: a control variable declared in the header of a for statement is only accessible within that loop's body and not outside of it.
Step-by-step explanation:
The statement 'A control variable that's declared in a for statement header is not accessible outside of the body of the for statement' is true. When you declare a variable in the header of a for loop, that variable is local to the loop block. For instance, in the Java programming language:
for (int i = 0; i < 10; i++) {
// i can be used here
}
// i cannot be used here; it is out of scope
The variable 'i' is only accessible within the for loop, and trying to use it outside of that scope will result in a compilation error since 'i' is not defined in that context.