Let n be an integer greater than 1 and consider the statement “A: 2" − 1 prime is necessary for n to be prime.”
(a) Write A as an implication.
(b) Write A in the form “p is sufficient for q.”
(c) Determine whether A is true or false.
(d) Write the converse of A as an implication.
(e) Determine whether the converse of A is true or false. [Hint: (2a)b − 1 = (2a −1)[(2a)b −l+ (2a)b −2 + ··· + 2a + 1].]
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