How do I prove that AB 0 if a 0 or B 0?

How do I prove that AB 0 if a 0 or B 0?

The zero property states that any number multiplied by 0 will result in 0. and, (0)0=0. so, if a=0, ab=0. if b=0, ab =0.

What property states that if AB 0 then a 0 or B 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.

Is AB 0 then?

If ab = 0, then a = 0 or b = 0. This statement is true. It is a property of the real numbers which was stated in class (without proof).

What form should you put the equation in to solve using zero product property?

You can use the Zero Product Property to solve any quadratic equation written in factored form, such as (a + b)(a − b) = 0.

How do you prove the 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. If a=0, then the property is true.

Which property is used in the statement if B 0 then 0 B?

The Zero Product Property simply states that if ab=0 , then either a=0 or b=0 (or both). A product of factors is zero if and only if one or more of the factors is zero. This is particularly useful when solving quadratic equations . x2+x−20=0 .

What happens if ab = 0?

If ab = 0 then a = 0 or b = 0. My proof is fairly straightforward. Assume for the sake of contradiction that a is not equal to 0 and b is not equal to 0, when you multiply a and b you get zero, but that is a contradiction because when you multiply two non zero numbe

Is it possible to prove that a <>0 and b <> 0?

In other words, at least one of the numbers a and b must be 0. This means that it impossible to prove that a <> 0 AND b <> 0 as a consequence of the assumption a.b = 0. If the algebraic structure is NOT a field, then a.b = 0 can happen. For instance in the ring Z/ (2. n. Z), n >= 1, the ring with 2. n elements (0, . . . 2.

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 it mean if a <> 0?

So, assuming that a.b = 0, we proved that: if a <> 0, then b = 0. By the symmetry in the argument, we can prove that: if b <> 0, then a = 0. In other words, at least one of the numbers a and b must be 0.