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7_ Prove: if a|b then &? | b...

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7_ Prove: if a|b then &? | b

7_ Prove: if a|b then &? | b



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Prove or disprove that if $a, b,$ and $d$ are integers with $d>0,$ then $(a+b)$ div $d=a \operatorname{div} d+b \operatorname{div} d$

So that's OK. Trust. Morning, baby. Square of you Use the desert spirit of experience more or fix. So this becomes maybe the whole square. This will raise spread. No. Again. Using this desert, you get more of the moral. Be square is equal to Marty. Or be the whole square. So you get more. The baby is equal, More trophy, more to be.

So this question we want to prove or disprove that if a divides BC then a divides me or a divide. See? So this fact is just simply not true. And to come up with a simple example as to why we have four divide six times by six. So the reason why is because six times six is 36 and we have 99 times four nine times for kids. You 36. So, therefore for does defied Divide 36. But Ford doesn't divide six. What doesn't The white six. So therefore this statement is false.

Okay, So, first statement, we want to show that if ain't divide B and B divides a then a easy to be or eggs even too negative. So to show this, if we have eight divides, quite be. This implies there exists an Internet sea in indigenous such that a c is it? It would be an opposite when eight would certainly be devised. A. This imply that their existence interject d images such that B d is equal to a So what we'll do is we'll substitute Well, sorry we will substitute be into here So we have a sea turns my deep is it to a expanding? We have a C D is equal to a But you notice that these two A's us are equal So they're the same letter. So that means by the identity property of multiplication CD must be equal to one. So this imply that CD is even to one. But since Cmdr. Vintage is by definition, we can't have any fractions. So we are left with. Either See is even to be easy to one or C is a city is a desert months one, because see India in stitches. Now what we'll do is we'll substitute this form into this one. First up. So we have seasons into one so easy to be so eight times one is one. And it substituted this one into the same one. Here we have 800 miles. One. So that's negative, eh? Is it? It should be or a easy to negative, and we've just proven their results.

Okay, So in this question, we want to prove that one divides a and a divide zero. So hey, who a divides be even any exists and into just see such that a C is equal to be so In this case, we want to prove that one device a so then way, let's see, is equal to ay a. Then C is into Jack because agent interject, then using the identity of property off multiplication one time CD 21 times Why a which is equal to a so therefore one divide a now to prove that a divide zero See that? See Beezer, then a thought C is equal to a But Sarah now using the zero property of multiplication, this is simply zero So devil, by definition, a divide is here.


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