Mathematical Logic M345P65

Added on - 15 Apr 2020

  • M345P65

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Discretemathematics
Table of ContentsQuestion-1............................................................................................................................................2(i)Single closed formula for axioms............................................................................................2(ii)Closed L formulas................................................................................................................2Question 2............................................................................................................................................3(i)First order................................................................................................................................3(ii) Consider the remove (a) and (b)...............................................................................................4Question -3...........................................................................................................................................4(i)L-structure...............................................................................................................................4(ii)b2 =a.....................................................................................................................................5(iii)The L- structure is provide k and c £ k..............................................................................5Question-4............................................................................................................................................5(i)A is countable...........................................................................................................................5(ii)A is an infinite......................................................................................................................6(iii)A∩B is a finite......................................................................................................................6References............................................................................................................................................7
Question-1(i)Single closed formula for axiomsGiven:L → language with qualitym → 2-array function symbole → constant symbolThe single closed formula for axioms group is expressed byLet the l language form is expressed as below:LG= {}andLG= {e,}*→ is a binary function and e → constant symbolLG- structure are of the form is given byM′=M, +Where + is defined as the binary function on M and the course of the interpretation of * inMM=M,m, +Let A is a closed formula forLG and LG is given by(ii)Closed L formulasGiven:A1 = (Q (√ −1) \ {0}; ·)A2 = (Z; +)A3 = (Q; +)A4 is the group of 2 × 2 invertible matrices over Q (under multiplication)A5 is the group of 2 × 2 invertible matrices of determinant 1 over QAi|= φji = j i, j{1 . . . 5}:Ai│=Φj = Φii = j , Φi= j={Φ1, Φ2, Φ3, Φ4, ..... Φ5}
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