If a, b belongs to Z then show that (1) if a/b and b/a this implies a = ±b. (2) if a/b and b/c then a/c. (3) if a/b then a/bc. (4) if a/b then ac/bc. (5) if a/b and a/c then a/bx+cy for x,y belongs to Z. (6) if a/b1+b2 and a/b1 then a/b2. (7) a/o (8) 1/a

Theorem:

If a, b belongs to Z then show that 
  1. If a/b and b/a this implies a = ±b. 
  2. If a/b and b/c then a/c.
  3. If a/b then a/bc.
  4. If a/b then ac/bc. 
  5. If a/b and a/c then a/bx+cy for x,y belongs to Z.
  6. If a/b1+b2 and a/b1 then a/b2.
  7.  a/o
  8. 1/a

Proof:

1

2 3 4

5

6 7

8

Amna Mughal

Graphic Designer | SEO Optimizer | Blogger | Java Developer | Photographer.

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