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March 30, 2017

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write the converse and contrapositive for the conditional statement below. decide whether each of the three statements is true or false. provide a counterexample for any false statement.

If n is a prime number, then n+1 is an even number

  • Math - ,

    converse
    if n+1 is even, then n is prime (not necessarily so false)
    if n = 9 then n+1 is even
    but 9 = 3*3

    contrapositive
    if n+1 Is not even, then n is not prime (true if original statement is true, which it is)

  • Math - ,

    but isnt 2 a prime # so 2+1=3 = odd

  • Math - ,

    Good thinking.
    I suspect that the original hypothesis should have stated greater than 2. That does not impact this problem because it is only asking for the converse and contrapositive.

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