The null factor law

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The null factor law

In: Mathematics

If a*b = 0, then a=0 or b=0.
Is there something you don’t understand here ?

This is basically a statement of De Morgan’s law. When I teach De Morgan’s law I like to use the following analogy.

Suppose we have a television set. There are two ways in which the television set can fail to show a picture. Firstly, it might be unplugged. Secondly, it might be broken itself.

Now if the television set is showing a picture, we can conclude two things. The television is plugged in AND the television is working.

If the television is not showing a picture, we get less information. We can conclude one of the following: The television is broken OR the television is not plugged in (or both these things).

In the case of the null factor law, if ab is not 0, then we can conclude that a is not 0 AND b is not 0 (since if one of them was then ab would be 0). On the other hand, if ab is 0, then we again get less information. Either a is 0, OR b is 0 (or both).