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Let n 2 Z with n > 1. Consider the statement R: Ä2n
18 May 2017
Let n 2 Z with n > 1. Consider the statement R: Ä2n
18 May 2017
consider the statement r: 2^n-1 is prime is necessary for n to be primei) write r as an implicationii)write r in the form p is sufficient for qiii) show that r is false
19 May 2017
http://mathworld.wolfram.com/Necessary.htmlIn general, "Statement A is necessary for Statement B" is equivalent to "Statement B implies Statement A".http://mathworld.wolfram.com/Sufficient.htmlIn general, "Statement C is sufficient for Statement D" is equivalent to "Statement C implies Statement D".For this question, we have 2 statements; "2^n-1 is prime", "n is prime".(i) "2^n - 1 is prime is necessary for n to be prime" is equivalent to:"n is prime implies 2^n - 1 is prime".(ii) Since r is equivalent to "n is prime implies 2^n - 1 is prime". This can also be written as: "n is prime is sufficient for 2^n - 1 to be prime".(iii) Statement r is (equivalent to): "n is prime implies 2^n - 1 is prime"n=4 implies 2^n -1 = 15, which is not prime. So Statement r is false.
27 June 2019
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