Let A and B each be sequences of letters: A = (a1,a2,...an) and B= (bị,b2,...,bn). Let I, be the set of integers: {1,2,...,n}. Make a formal assertion for each of the following situations, using...

Extracted text: Let A and B each be sequences of letters: A = (a1,a2,...an) and B= (bị,b2,...,bn). Let I, be the set of integers: {1,2,...,n}. Make a formal assertion for each of the following situations, using quantifiers with respect to Tn. For example, Vi E I, :Vj€ I,:a;=a; asserts that all letters in A are identical. You may use the relational operators “=", “#", and “<", as="" well="" as="" our="" usual="" operators:="" "v",="" “a".="">< is="" “less="" than"="" for="" english="" letters:="" c="">< d="" is="" true,="" and="" c="">< c="" is="" false.)="" you="" may="" not="" apply="" any="" operators="" to="" a="" and="" b.="" for="" example:="" a="B" is="" not="" allowed,="" and="" a="" c="" b="" is="" not="" allowed.="" (a)="" the="" letters="" of="" a="" are="" lexicographically="" sorted.="" (b)="" the="" letters="" of="" a="" are="" not="" lexicographically="" sorted.="" (do="" this="" without="" using="">