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2 Propositional equivalences Usc logical to that (p Note: may sabmilt an ansiver in inspera, or handentitten solution. Start st (e - st - - 31 Ihr DE ecch ent the andise the prevous nto , logicale compound prepositor. Apoly ony quvalence per in Inspera the TAX mey be in the aditter il (cque A of 2 7 Set identities Ldt A n. and 30 sets ohr the same 52 U. Use = bulder notation and to important: 720 may submit an answer ininspera or a handeritten solution on expression for a or the Starleach subsequent 31 equelly symbol and use alogical 10 the into ACI inded persor 1you type your in Inspera the bizwing Ick sembris be ascrui no oquation oditer the r. T 10 Image, Pre-image Suppose f : R R where f(x) - 1. If S = {o|12. If T = ((3.4,5), ind f -(1) . 12 Euclidean algorithm Use the Bucideon find ged(123,277) Note: You may submit an answer In inspera, or a handwritten solution al sleps of your calculal om caplicity, adting noe ness as required of you in use the For Instonce 1-2-111 2=1-2+0 FIII in your answar here 15 Mathematical induction mathematical induction to prowe that 52,38 2) = for all Integens n. 1 = Note: You may submit an answer in Inspera, or a handwillen solution FIII in your answer here 17 Structural induction Let S be the subset of the ordered pa s of integers derined recursively by Bess step (0.0) E S Recursivo If (a,6) : S. then (a c 1) c Send ia 1.6 1) C S. a) List the elements of 8 produced by the frst three applications of the recursive definition b) Use structural induction to a < bahenever (a.ò) € S Note: You may submit an answer In Inspera, or handwritten solution.

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