A natural number n is said to be a Pierre number when it can be expressed...

 

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A natural number n is said to be a "Pierre number" when it can be expressed as 2^(2^k) + 1 for some integer k. (a) Write a predicate PierreNumber(n) that is True if and only if n is a Pierre number. (b) Express the statement "All Pierre numbers are odd." using predicate logic. You may use the predicate PierreNumber, the predicate = and logical operators, but may not use other predicates (like Odd or Even). (c) Express the statement "There is not a largest Pierre number." using predicate logic. You may use the predicate PierreNumber and the standard inequality predicates but may not use other predicates. (d) Express the statement "Only the five smallest Pierre numbers are prime." using predicate logic. You may use the predicate Prime(n). The smallest Pierre number is 3. (Hint: you may find this question easier if you don't use your predicate PierreNumber(n). Use the Pierre number definition instead.) A natural number n is said to be a "Pierre number" when it can be expressed as 2^(2^k) + 1 for some integer k. (a) Write a predicate PierreNumber(n) that is True if and only if n is a Pierre number. (b) Express the statement "All Pierre numbers are odd." using predicate logic. You may use the predicate PierreNumber, the predicate = and logical operators, but may not use other predicates (like Odd or Even). (c) Express the statement "There is not a largest Pierre number." using predicate logic. You may use the predicate PierreNumber and the standard inequality predicates but may not use other predicates. (d) Express the statement "Only the five smallest Pierre numbers are prime." using predicate logic. You may use the predicate Prime(n). The smallest Pierre number is 3. (Hint: you may find this question easier if you don't use your predicate PierreNumber(n). Use the Pierre number definition instead.)

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