Question

QUESTION 1 Check the box next to EXACTLY THOSE claims that are TRUE: Goedel numbering maps injectively the set of all finite sequences of natural numbers into the set of natural numbers. There exist Goedel numbers that are not divisible by 3. It n is the image of a sequence < x1, x2, x3, x4 > under Goedel numbering, then 11xn is the image of the sequence < x1, x2, x3, x4, 1> Whenever a Goedel number is divisible by 11, it is also divisible by 5. Every Goedel number is divisible by 2. There exist infinitely many finite sequences of natural numbers that do not have an image under Goedel numbering Whenever a Goedel number is divisible by 7, then it is the image of a sequence whose length is greater than For every natural number n, there exist infinitely many finite sequences of natural numbers that are mapped to n under Goedel numbering There exist infinitely many natural numbers that are not images of any sequence under Goedel numbering.

Answer 1

Ans: The TRUE statements are - 1. Goedel numbering maps injectively T the set of all finite sequences of natural numbers into the set of natural numbers. There that enist Goedel numbers are not dirisible by si I of n is the image of a sequence xx, ,X2, X3, No 7 under Goedel numbering then u xn is the image || at - диетсе, 4x4, 3, 4 4 4) 1 Every Goedel number is dir isible by A2 5. There exist infinitely many tinite sequences of natural numbers that I do not have an image under Goedel 6. For every natural number n there Fenists Clinifinitly many finite sequences of natural numbers that are mapped to n under Goedel membering,