Theory and Problems in Discrete Mathematics (34)

# Theory and Problems in Discrete Mathematics (34) - the...

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the conclusion by way of VE at line 11. We whole the proof by the use of discharging the hypothesis and reasserting the conclusion through 3E at line 12. The reader will have got to confirm that step 12 obeys the 3E rule. THE PREDICATE CALCULUS 7.18 show: [CHAP. 7 3xFx v 3xGx 1 3x(Fx V Gx) answer 1 2 3 4 5 Fa 3y Lay Lab (;a Ga & Lab 3y(Ga & Lay) 3x3y(Gx & Lxy) 3x3y(Gx & Lxy) 3x3y(Gx & Lxy) H (for 3E)

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1 QE 3 &E 4, 5 --E H (for 3E) three &Ei 7, eight &I 9 31 10 311 6, 7-11 3E 2, 3-12 3E This proof requires two makes use of of 3E, one for each existential quantifier in the assumptions. We at step 3 with the aid of hypothesizing a consultant illustration of
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• Spring '14
• mathematics, Theory, Problems, Discrete, Predicate logic, Quantification, Universal quantification, Gx, Lxy

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