Question

That if x • y = 0, then either x or y is 0. You have this problem for homework: 5x=0 and reason that x must be 0. What type of reasoning is this?

Answer 1

We are using an inductive reasoning, as a matter of fact, we know that "For a product to be zero, one of its members must be zero"

So x*y = 0 if x=0 OR y=0

Now, we know that
5x=0.
So, recalling the Zero-product property (derived from the axioms of real numbers) we are able to say that
5x=0 => x=0.

Answer 2

\[5x=0 \Rightarrow x = 0\] since, \[5 \neq 0 \]

Answer 3

5x=0
⇒x=0, since, 5≠0

we are actually dividing both sides of the equation by 5. Hence,the implication.