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Given the univense U={w1,w2,w3} where: - wh is the world in which Sophia is a matbermatician, Keith is a phonologist, and Lotus is a syatactician - w2 is the world in which Sophia and Keith are pragmaticists and Lotus is a syztactician - wo is the world in which Sophia is a sociolinguist, Lotus is a physicist, and Keith is a phonologist - R is the relation between worlds in which if Sophia is linguist in the first one, then both Sophia and Lotus are linguists in the second one: R={w1,w1,w1,w2,w1,w3,w2,w2,w3,w2}. i. Provide the truth conditions of the following propositions, i.e. the set of worlds in which the propositions are true (skill 2.1): a. There are at least three specialisations in this world. S1= b. Sophia and Keith have the same specialisation. S2= c. Sophia is a linguist. S3= d. Sophia is a linguist or a mathematician. S4= ii. Perform the following operations on sets (ssill 6.1): a. S1S2= b. S1S3= c. S1s2 d. S2S1= e. S2S1= f. S2v=S2=S2r= iii. Eviluate the following claims ahout sets as being troe or false, and justify your answer (skill 6.2): 3 a. {S2} is a member of {S1}. b. {S2} is a suthet of S1. c. S2 is a proper subeset of S1. d. S2 is a subet of {S1}. iv. Provide the property notation of the follewing set (skill 6.4): S5={w2,w3} v. Provide the list notation of the following set (skill 6.5): S6={wi Lotus is a syntactician in wi} vii. Provide the characteristic functions of S3 and of R (sbnfinkelized rightto-lett) (skill 6.6). viii. Provide (list the elements of) the characteristic set of the following functions (the second is shnfinkelized right-to-lett) (skill 6.7): fsour=w11w20w30fQmar=w1w10w21w31w2w10w20w30w3w10w21w31 Given the univense U={w1,w2,w3} where: - wh is the world in which Sophia is a matbermatician, Keith is a phonologist, and Lotus is a syatactician - w2 is the world in which Sophia and Keith are pragmaticists and Lotus is a syztactician - wo is the world in which Sophia is a sociolinguist, Lotus is a physicist, and Keith is a phonologist - R is the relation between worlds in which if Sophia is linguist in the first one, then both Sophia and Lotus are linguists in the second one: R={w1,w1,w1,w2,w1,w3,w2,w2,w3,w2}. i. Provide the truth conditions of the following propositions, i.e. the set of worlds in which the propositions are true (skill 2.1): a. There are at least three specialisations in this world. S1= b. Sophia and Keith have the same specialisation. S2= c. Sophia is a linguist. S3= d. Sophia is a linguist or a mathematician. S4= ii. Perform the following operations on sets (ssill 6.1): a. S1S2= b. S1S3= c. S1s2 d. S2S1= e. S2S1= f. S2v=S2=S2r= iii. Eviluate the following claims ahout sets as being troe or false, and justify your answer (skill 6.2): 3 a. {S2} is a member of {S1}. b. {S2} is a suthet of S1. c. S2 is a proper subeset of S1. d. S2 is a subet of {S1}. iv. Provide the property notation of the follewing set (skill 6.4): S5={w2,w3} v. Provide the list notation of the following set (skill 6.5): S6={wi Lotus is a syntactician in wi} vii. Provide the characteristic functions of S3 and of R (sbnfinkelized rightto-lett) (skill 6.6). viii. Provide (list the elements of) the characteristic set of the following functions (the second is shnfinkelized right-to-lett) (skill 6.7): fsour=w11w20w30fQmar=w1w10w21w31w2w10w20w30w3w10w21w31