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3 prove by providing an argument or disprove by finding...

Question: 3 prove by providing an argument or disprove by finding...

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(3) Prove by providing an argument or disprove by finding a counterexample to the following statements. a,b are positive integers and r, s are integers. (a) if rs (mod a), then sr (mod a) (b) if rs (mod a), then s (mod ab) (c) if r s (mod ab), then r 8 (mod a) (d) if rs (mod a), then krks (mod a) e) if kr ks (mod a), then r s (mod a) (f) if rs + ab-# 1 then r., 1 (mod a) (g) there exists an r E (0,1,2,..a-1) such that s a (mod a) (h) if s 0 (mod a) then a divides s. (i) if s 0 (mod a) then s divides a G) if b 0 (mod a) and a (mod b), then a -b.

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