EmshoffA_MTH525_Module_2_CT_Option1 - Ashley Emshof CSU Global MTH525 Discrete Mathematics Instructor Brian Stout 1 The distributive property of

EmshoffA_MTH525_Module_2_CT_Option1 - Ashley Emshof...

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Ashley Emshof July 28, 2017 CSU Global MTH525 Discrete Mathematics Instructor: Brian Stout
1. The distributive property of multiplication over addition holds for: Zm where m >1. ( a + b m ) x c m = ( ( a + b ) mod m ) x c m ¿ ( amod m + bmod m ) x c m ¿ amod m x c + bmod m x c m m ¿ ( amod m x c ) mod m + ( bmod m x c ) mod m ¿ ( a x c m ) mod m + ( b x c m ) mod m ¿ ( a x c m ) +( b x c m ) 2. That Zm with addition modulo m satisfies the closure, associative, and commutative properties. Closure: a + b m = ( a + b ) mod m Since ( a + b ) mod m Z m Therefore, if a and b belong to Zm, then

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