Final answer:
The statement that all programs can be written using only the three structures of sequence, selection, and iteration is true. These structures are the cornerstone of structured programming and are universally applicable across different programming languages, enabling complex algorithms to be built from simple operations.
Step-by-step explanation:
The statement "It has been proven by a group of mathematicians that all programs can be written using only three structures" is TRUE. These structures are sequence, selection, and iteration. In computer programming, these structures are fundamental for controlling the flow of execution and enabling the construction of complex algorithms from simple, well-defined operations. The sequence structure refers to a series of actions that execute one after another. Selection is the use of conditional statements that allow the program to take different paths based on whether a condition is true or false. Iteration involves loops that repeat a block of code as long as a certain condition remains true.
These three control structures form the basis of structured programming, which is an approach to writing software where control structures are combined in block-structured ways, without using goto statements and thus making programs easier to understand and maintain. This principle holds true for almost all modern programming languages and paradigms, showing the fundamental and universal nature of sequence, selection, and iteration in creating software.