QUESTION 1 18 point Complete the sentences below so as to obtain correct claims, by writing into each empty space an appropriate string of decimal digits that represents an integer (no whitespace, no punctuation, no redundant zeros). Where it is impossible to find an integer that makes the claim true, write NONE in that space. The Goedel number of the sequence is equal to: 23100 and the smallest prime with which this Goedel The Goedel number of the sequence is equal to: 30 number is not divisible is equal to: 7 ; the Let the Goedel number of a sequence x be equal to 50820. The length of the sequence x is equal to: 5 first element of x is equal to: 1 ; the largest element of x is equal to: 1 Let the Goedel number of a sequence be equal to n. The Goedel number of the sequence is equal to: nx 12 Let the Goedel number of a sequence be equal to m. The Goedel number of the sequence is equal to: mx 55 Let ; be the Goedel number of a sequence z, and let j = 66 p, for some natural number p. The length of the sequence z is greater than or equal to: 5 QUESTION 2 18 points Check the box next to EXACTLY those claims that are TRUE. There exists a sequence s= (x, y, z, w) of natural numbers and a natural number n such that n is the image of s under Goedel injection, and n 70 n. Let s= (x, 1, z) be a sequence of natural numbers. There exists a natural number n such that image of s under Goedel injection is equal to n, and n is divisible by 18. Let s = (x, y) be a sequence of natural numbers. Let s=(x, y, z, w) be a sequence of natural numbers. There exists a natural number n such that the image of s under Goedel injection is equal to n. Let s= (x, y, z, v) be a sequence of natural numbers, and let n be the image of s under Goedel injection. On is always divisible by 21 and 22. Let s= (x, y, z) be a sequence of natural numbers, and let n be the image of s under Goedel injection. There exists a natural number k such that image of the sequence (x, y, z, 1, 1) under Goedel injection is equal to k, k