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Write the contrapositive statements to each of the following.  Then prove each of them by proving their respective contrapositives. ...


Write the contrapositive statements to each of the following.  Then prove each of them by proving their respective contrapositives.  In both statements assume x and y are integers.


a. If  the product xy is even, then at least one of the two must be even.

b. If the product xy  is odd, then both x and y must be odd.

3. Write the converse the following statement.  Then prove or disprove that converse depending on whether it is true or not.  Assume x and y are integers.

a. If  x and y are even then x+y is even.

4.  Write a useful negation statements to each of the following.    In both statements assume x and y are integers. Prove that these negations are false! 

a. If  the product xy is even, then at least one of the two must be even.

b. If the product xy  is odd, then both x and y must be odd.


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