Final answer:
The statement that if 'a' is less than 'b', and 'b' is less than 'c', then 'a' must be less than 'c' is a) true, based on the transitive property of inequalities. This principle applies universally in mathematical contexts and serves as a foundation for comparing values.
Step-by-step explanation:
If given a < b and b < c, it logically follows that a < c. This statement is true and is known as the transitive property of inequalities in mathematics. Here's why: if 'a' is less than 'b', and 'b' is less than 'c', there is no value that 'b' can have that allows 'a' to be greater than or equal to 'c', as 'b' serves as a middle term smaller than 'c' but larger than 'a'. Thus, 'a' must be less than 'c' as well.
The transitive property is fundamental in mathematics, particularly in algebra and number theory, and it is used to make comparisons between values and to solve inequalities. Inequality rules apply not only to numbers but also to other instances involving order, such as forces in physics or comparing areas in geometry.
Referencing provided information, we can see that this principle applies to various scenarios - for example, when comparing magnitudes of force or areas. In every case, the transitive property clarifies the relationship between multiple elements when they are ordered in magnitude or size. Therefore, the correct option in the final answer to the question 'If a < b and b < c, then a < c.' is a) True.