Question

a/b+0=0+a/b . 0 is known as​

Answer 1

Answer:

nahi aata ?????

?????????????

Answer 2

Answer:

How do I prove that ab=0 if a=0 or b=0?

I’m not entirely sure what you are asking here. Proving that if a=0 or b=0 then ab=0 is pretty easy, so I’m going to guess that you are more interested in how to prove that if ab=0 then a=0 or b=0 .

First, let’s note that this will be true in any field, and thus we can use all of the field axioms to help us prove this.

We want to prove that ab=0 in any field.

Let’s use an indirect proof to solve this.

Proof:

Suppose that ab=0 in a field. Let’s consider two cases: a=0 or a≠0.

Case 1: If a=0 , we are done because we have shown that either a=0 or b=0 .

Case 2: If a≠0 , then we know that a has a multiplicative inverse a−1 because any number in a field that it is not 0 has a number by which it can be multiplied to get 1 , a⋅a−1=1 , which is the definition of a multiplicative inverse.

Now let’s consider the statement:

a−1⋅(ab)=0⋅a−1.

Let’s solve:

We can regroup our products on the left side because multiplication is associative in a field to get:

(a−1⋅a)⋅b=0⋅a−1.

Again, any number multiplied by its multiplicative inverse is 1 , so on the left we have:

1⋅b=0⋅a−1.

Next, we also know that any number times 0 will just be 0 so we can adjust the right side as:

1⋅b=0.

And with some final clean up we have:

b=0

Which again tells us that either a=0 or b=0 if ab=0 in a field.

Once more, this is not exactly what the question was asking, but the converse of this question is much more difficult and interesting to prove