Consider the statement A If n is an integer nn1 is not an in

Consider the statement A: \"If n is an integer, n/(n+1) is not an integer.\"

a. Is A true or false? Either prove true, or give a counterexample to prove false.

b. Write down the converse, the contrapositive, and the negation of A. Which of these is true? Which is false? Justify each answer with a proof or a counterexample.

Solution

Answer:

Consider the statement A : \"If n is an integer, n/(n+1) is not an integer.\"

Then the statement A is true.

ex : if n = 2 an integer then n+1 = 3 and n/(n+1) = 2/3 is not an integer.

b) The converse of the statement A is \" if n/(n+1) is not an integer then n is an integer \"

    it is true

    The contrapositive of the statement A is \" if n/(n+1) is an integer then n is not an integer \"

    it is true

    The iverse of the statement A is \"If n is not an integer, then n/(n+1) is an integer.\"

     it is false.

if n = 2/3 then n/(n+1) = 2/5 which is not an integer