PLEASE ANSWER ALL PARTS

PLEASE ANSWER ALL PARTS

PLEASE ANSWER ALL PARTS

PLEASE ANSWER ALL PARTS

PLEASE ANSWER ALL PARTS

3. Recall that S is defined as the set of all RNA strands, strings made of the bases in B = {A, U,G,C}. Define the functions mutation, insertion, and deletion as described by the pseudocode below: i procedure mutation (by...bni a RNA strand, k: a positive integer, b: an element of B) 2 for i:=1 ton 3 if i = le S else 7 return ci... {The return value is a RNA strand made of the values} 1 2 3 6 6 7 procedure insertion(bu...bn a RNA strand, k: a positive integer, b: an element of B) if > n for i:=1 ton = b Cn+1 = b else for i:= 1 to k-1 C = b Cheb for i:= k +1 to n +1 bi1 return ci...C+1 {The return value is a RNA strand made of the values 10 12 1 procedure deletion(bi..bra: a RNA strand, k: a positive integer) 2 if kn 3 m = n for i = 1 ton 6 else 7 m := n-1 8 for i:= 1 to k-1 10 11 12 for i:= k to n-1 c = +1 return ci...cm {The return value is a RNA strand made of the values} For this question, we will use the following predicates. FA with domain S is defined recursively by: Basis step: F.(A) =T, F.(C) = F (G) = F.(U)= F Recursive step: If s ES and b E B, then F (sb) = F. (s) Pauc with domain S is defined as the predicate whose truth set is the collection of RNA strands where the string AUC is a substring (appears inside s, in order and consecutively) L with domain S xZ+ is defined by, for s ES and n e Z+, ( L(s,n) = F if rnalen(s) =n otherwise Mut with domain S x S is defined by, for si e S and s2 ES, Mut(S1, S2) = 3k 2+36 B( mutation(s, k, b) = s2) Ins with domain SxS is defined by, for si e S and s2 ES, Ins(S1, S2) = 3k EZ+36 B( insertion(s,k,b) = 82 ) Del with domain S x S is defined by, for si e S and s2 ES, Del(S1, S2) = 3k Z+( deletion(s1,k) = 52 ) (a) Which of the following is true? (Select all and only that apply.) i. F.(AA) ii. F.(AC) iii. F (AG) iv. F.(AU) v. FA (CA) vi. F.(CC) vii. FCG viii. FACU) (b) Which of the following is true? (Select all and only that apply.) i. 3s (Pauc(s)) ii. Vs (Pauc(s)) iii. 3s (-Puc(s)) iv. Vs (Pauc(s)) v. as (Pauc(s)) vi. Vs (Pauc(S) vii. 3s (-Pauc(s)) viii. Vs (Pauc(s)) (c) Which of the following is true? (Select all and only that apply.) i. Es ES 3n e Z+ (L(s, n)) ii. Is ES Vn e Z+ (L(s, n)) iii. Vn e Z+ Is ES (Ls, n)) iv. Vse S En e Z+ (L(s, n)) v. In e Z+ Vs ES (L(s, n)) vi. Vs ES Vn e Z+ (L(s. n)) (d) Which of the following is true? (Select all and only that apply.) i. Is ES Mut(s,s) ii. Vs ES Muts,s) iii. s ES Ins(s, A) iv. Is ES Ins(A, s) v. Is ES Del(s, A) vi. Vs ES Dels, A) 3. Recall that S is defined as the set of all RNA strands, strings made of the bases in B = {A, U,G,C}. Define the functions mutation, insertion, and deletion as described by the pseudocode below: i procedure mutation (by...bni a RNA strand, k: a positive integer, b: an element of B) 2 for i:=1 ton 3 if i = le S else 7 return ci... {The return value is a RNA strand made of the values} 1 2 3 6 6 7 procedure insertion(bu...bn a RNA strand, k: a positive integer, b: an element of B) if > n for i:=1 ton = b Cn+1 = b else for i:= 1 to k-1 C = b Cheb for i:= k +1 to n +1 bi1 return ci...C+1 {The return value is a RNA strand made of the values 10 12 1 procedure deletion(bi..bra: a RNA strand, k: a positive integer) 2 if kn 3 m = n for i = 1 ton 6 else 7 m := n-1 8 for i:= 1 to k-1 10 11 12 for i:= k to n-1 c = +1 return ci...cm {The return value is a RNA strand made of the values} For this question, we will use the following predicates. FA with domain S is defined recursively by: Basis step: F.(A) =T, F.(C) = F (G) = F.(U)= F Recursive step: If s ES and b E B, then F (sb) = F. (s) Pauc with domain S is defined as the predicate whose truth set is the collection of RNA strands where the string AUC is a substring (appears inside s, in order and consecutively) L with domain S xZ+ is defined by, for s ES and n e Z+, ( L(s,n) = F if rnalen(s) =n otherwise Mut with domain S x S is defined by, for si e S and s2 ES, Mut(S1, S2) = 3k 2+36 B( mutation(s, k, b) = s2) Ins with domain SxS is defined by, for si e S and s2 ES, Ins(S1, S2) = 3k EZ+36 B( insertion(s,k,b) = 82 ) Del with domain S x S is defined by, for si e S and s2 ES, Del(S1, S2) = 3k Z+( deletion(s1,k) = 52 ) (a) Which of the following is true? (Select all and only that apply.) i. F.(AA) ii. F.(AC) iii. F (AG) iv. F.(AU) v. FA (CA) vi. F.(CC) vii. FCG viii. FACU) (b) Which of the following is true? (Select all and only that apply.) i. 3s (Pauc(s)) ii. Vs (Pauc(s)) iii. 3s (-Puc(s)) iv. Vs (Pauc(s)) v. as (Pauc(s)) vi. Vs (Pauc(S) vii. 3s (-Pauc(s)) viii. Vs (Pauc(s)) (c) Which of the following is true? (Select all and only that apply.) i. Es ES 3n e Z+ (L(s, n)) ii. Is ES Vn e Z+ (L(s, n)) iii. Vn e Z+ Is ES (Ls, n)) iv. Vse S En e Z+ (L(s, n)) v. In e Z+ Vs ES (L(s, n)) vi. Vs ES Vn e Z+ (L(s. n)) (d) Which of the following is true? (Select all and only that apply.) i. Is ES Mut(s,s) ii. Vs ES Muts,s) iii. s ES Ins(s, A) iv. Is ES Ins(A, s) v. Is ES Del(s, A) vi. Vs ES Dels, A)