Question

If x, y ∈ R and xy = 0, then prove that x = 0 and y = 0.​

Answer 1

Step-by-step explanation:

How do I prove x•y=0 then x=0 or y=0?

One way is to prove it by contradiction, or assuming there is a case that violates the statement and finding a false statement that shows a case can't exist.

We are going to prove that if x * y = 0, then x = 0 or y = 0. Let's assume that there exists an x and y such that x != 0, y != 0 and x * y = 0. Dividing both sides of the equation by y gives us x * y / y = 0 / y = x = 0 because y != 0. x = 0 is a contradiction to x != 0. Therefore, if x * y = 0, then x = 0 or y = 0.

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