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20190213_163801.jpg - 19 30 Determine to love tore of False...

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Unformatted text preview: \ ( 19 - 30 Determine to love tore of False_ Prove the statement directly from` the definitions if it is tome , and give a counter example if false. 20 ) The sum of any three consecutive images is divisible by 3. (Two integers are consecutive if , and only if , one is more than the other. ( ox ) + ( a + 1 ) + ( 9 + 2 ) = ( 3 0 + 3 ) =\ 3 ( a + 1 )| So the statement is true because 3 is the divisor we are looking for and att can be an integer . ..!` 24 ) for all integers arb , and C , if albo and all than a | ( 25 - 30 ) . By definition of divisibility` we know that b = as and C = as for some integers I and S. so 26 - 36 = 2car ) - 3 ( As ) - 2 ar - 3 95 `A = = = ( 25- 35) Since { and } on both integers and I and I are both interers , their products will be integers and the equation is true by the definition of divinable 281 for all integers Garb , and `` if albe then all of all FALSE. if a : 8 6 : 2, 6 : 4 \\ 5 . 6: 8 4 160 is true but all and alc are false...
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  • Fall '19
  • NoProfessor
  • Addition, Negative and non-negative numbers, Prime number, Integral domain

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