Final answer:
The statement is true applying both the Associative and Commutative Properties of multiplication, which support reordering and regrouping factors without changing the product.
Step-by-step explanation:
The correct answer is option (a) True. In mathematics, particularly when dealing with properties of real numbers, the statement (r · s) · t = t · (s · r) can be proven true using the Associative Property of multiplication and the Commutative Property of multiplication. The Associative Property states that the way in which factors are grouped in a multiplication problem does not change the product, meaning (r · s) · t is equivalent to r · (s · t). The Commutative Property indicates that the order of the factors does not affect the product, allowing us to write s · r instead of r · s. Therefore, by applying both properties, we validate the given statement.
In order to determine whether the statement (r.s).t = t.(s.r) is true or false, we can use deductive reasoning and examine the properties of real numbers.
In this case, we can use the associative property of real numbers, which states that for any real numbers a, b, and c, (a.b).c = a.(b.c). By applying this property, we can see that (r.s).t = r.(s.t), and t.(s.r) = (t.s).r. Since both expressions are equal, the statement (r.s).t = t.(s.r) is true.
Therefore, the property of real numbers needed to show the expressions are equivalent is the associative property.