Use deductive reasoning to tell whether the statement shown below is true or false. If it is true, indicate which property or properties of real numbers are needed to show the expressions are equivalent.
For all real numbers r, s, and t, (r x s) x t = t x (s x r).
Select the correct answer below.
A.
The statement is true. The expressions can be shown to be equivalent using only the Associative Property of Multiplication.
B.
The statement is true. The expressions can be shown to be equivalent using only the Commutative Property of Multiplication.
C.
The statement is true. The expressions can be shown to be equivalent using both the Commutative Property of Multiplication and the Associative Property of Multiplication.
D.
The statement is false.
C. The statement is true. The expressions can be shown to be equivalent using both the Commutative Property of Multiplication and the Associative Property of Multiplication.
The correct answer is A.
The statement is true, and the expressions can be shown to be equivalent using only the Associative Property of Multiplication.
The Associative Property of Multiplication states that for any real numbers a, b, and c, (a x b) x c = a x (b x c). Therefore, by applying this property to the given statement, we can conclude that (r x s) x t = t x (s x r).
To determine whether the statement is true or false, we can use deductive reasoning and examine the properties of real numbers.
Let's consider the statement: (r x s) x t = t x (s x r).
To show that both expressions are equivalent, we need to demonstrate that the order of multiplication does not matter. This property is called the Associative Property of Multiplication.
Using deductive reasoning, we can see that the statement is true since the Associative Property of Multiplication states that for any real numbers a, b, and c, (a x b) x c = a x (b x c).
Therefore, the correct answer is:
A. The statement is true. The expressions can be shown to be equivalent using only the Associative Property of Multiplication.