If rstv=1 and stuv= 0 which of the following must be true?

A. r<1
B. s<1
C. t<1/2
D. u=0
E. v=0
I don't know what steps I should use to solve this problem.

The only way for stuv to be zero if if one or more of the factors are zero. Considering rstv=1, then r, s, t, v cannot be zero, so therefore, u has to be zero.

check my thinking.

To solve this problem, we can break down the given equation into individual variables and use logical deduction.

Given:
rstv = 1
stuv = 0

First, let's examine the first equation: rstv = 1

We know that the product of four numbers (r, s, t, and v) is equal to 1. In order for a product to equal 1, at least one of the numbers must be equal to 1.

Moving on to the second equation: stuv = 0

Here, we have a product of four numbers (s, t, u, and v) equal to 0. In order for the product to equal 0, at least one of the numbers must be equal to 0.

Now, let's analyze the answer choices:

A. r < 1:
We cannot determine if this is true or false based on the given information. We only know that one of the variables must be equal to 1, but we don't have any information on the other variables.

B. s < 1:
We also cannot determine if this is true or false based on the given information. Similar to option A, we don't have sufficient information to determine the value of s.

C. t < 1/2:
Again, we cannot determine if this is true or false based on the given information. We know nothing about the value of t.

D. u = 0:
This can be true. We know that one of the variables must be 0 in order for the product stuv = 0. We can conclude that u = 0.

E. v = 0:
This can also be true. Similar to option D, we know that one of the variables must be 0 in order for the product stuv = 0. So, v = 0.

In summary, the options that must be true based on the given information are:

D. u = 0
E. v = 0

Therefore, the correct answer is (D) and (E).