[Get Solution]Mathematics-Computer Science

Mathematics-Computer Science 4215H – Mathematical Logic Trent University, Winter 2021Assignment #6 Due on Friday, 5 March.Do all of the following problems, all of which are straight out of the textbook0 (which explains the numbering), reproduced here for your convenience.5.1. [Problem 5.1] Which of the following are terms of one of the languages defined in Examples 5.1 and 5.2? If so, which of these language(s) are they terms of; if not, why not? (1) ·v2 (3) |1 + v30 (5) + + · + 00000 [1.5 = 3×0.5 each]5.2. [Problem 5.2] Choose one of the languages defined in Examples 5.1 and 5.2 which has terms of length greater than one and determine the possible lengths of terms of this language. [2]5.4. [Problem 5.4] Which of the following are formulas of one of the languages defined in Examples 5.1 and 5.2? If so, which of these language(s) are they formulas of; if not, why not? (1) = 0 + v7 · 1v3 (3) (|v20 ?·01) (5) < +01|v1v3 [1.5 = 3×0.5 each]5.6. [Problem 5.6] Choose one of the languages defined in Examples 5.1 and 5.2 and de- termine the possible lengths of formulas of this language. [Do this for the language you chose in Problem 5.2.] [2]5.8. [Problem 5.8] In each case, write down a formula of the given language expressing the given informal statement. (2) “There is an empty set” in LS. [1] (4) “n0 = 1 for every n different from 0” in LN . [1]5.9. [Problem 5.9] Define first-order languages to deal with the following structures and, in each case, an appropriate set of axioms in your language: (2) Groups. [3]5.11. [Problem 5.11] Give a precise definition of the scope of a quantifier. [2]5.12. [Problem 5.12] Which of the formulas you gave in solving Problem 5.8 are sentences? [1 = 2×0.5 each][Total = 15]0 A Problem Course in Mathematical Logic, Version 1.6.         So much stress and so little time? We’ve got you covered. Get your paper proofread, edited or written from scratch within the tight deadline.