What states if AB equal zero then 0 equals B or 0?

Zero Product Property
The Zero Product Property states that if the product of two numbers is zero, then at least one of the numbers is zero. In symbols, where a and b represent numbers, if ab=0, then a = 0 or b=0. This steps below provide a proof of this property starting with the equation ab=0.

Is this true in general that ABAC implies BC If A is not invertible?

AB=AC⇒A−1AB=A−1AC⇒B=C. If A is not invertible, AB=AC⇒B=C does not work.

Which is not equal to A to B?

The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality. It does not say that one is greater than the other; it does not even require a and b to be member of an ordered set.

How to prove “if a then B”?

Three Ways to Prove “If A, then B.” A statement of the form “If A, then B” asserts that if A is true, then B must be true also. If the statement “If A, then B” is true, you can regard it as a promise that whenever the A is true, then B is true also. Most theorems can be stated in the form “If A, then B.”

How do you prove if a is true B is false?

Therefore B is true. CONTRAPOSITIVE PROOF. The idea is that if the statement “If A, then B” is really true, then it’s impossible for A to be true while B is false. Thus, we can prove the statement “If A, then B” is true by showing that if B is false, then A is false too.

What is the proof that ab = 0?

We have to show that if ab = 0, then either a = 0 or b = 0, and we have to show that if a = 0 or b = 0, then ab = 0. Let’s do the second one first because it’s easier. Proof: Given a = 0 or b = 0, to show that ab = 0. If we know that 0 times anything is 0, then we can conclude that.

What does “if a then B is true” mean?

If the statement “If A, then B” is true, you can regard it as a promise that whenever the A is true, then B is true also. Most theorems can be stated in the form “If A, then B.” Even if they are not written in this form, they can be put into this form.