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, left parenthesis r times s right parenthesis times t equals t times left parenthesis s times r right parenthesis.
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Part 1
Select the correct answer below.
A. The statement is true. The expressions can be shown to be equivalent using only the Commutative Property of Multiplication.
B. The statement is true. The expressions can be shown to be equivalent using only the Associative Property of Multiplication.
D. The statement is false.
C. The statement is false.
This is because the statement is claiming that for all real numbers r, s, and t, the expression (r * s) * t is equal to t * (s * r). However, this is not always true.
For example, if we let r = 2, s = 3, and t = 4, we have:
(2 * 3) * 4 = 6 * 4 = 24
t * (s * r) = 4 * (3 * 2) = 4 * 6 = 24
In this example, the expressions are equivalent. However, if we let r = 0, s = 1, and t = 2, we have:
(0 * 1) * 2 = 0 * 2 = 0
t * (s * r) = 2 * (1 * 0) = 2 * 0 = 0
In this example, the expressions are not equivalent. Therefore, the statement is false.