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1. (a) Sketch the construction tree of the following propositional formula o -((¬r V (r ^ ¬p)) + (¬¬¬q → r)). Give its complexity c(4) and list all of its subformulas (without repetition). How many distinct subformulas are there? (b) Use structural induction on the complexity of formula y to show that the number of occurrences of the symbol A in p is less than or equal to the number of left brackets in y.

1. (a) Sketch the construction tree of the following propositional formula o -((¬r V (r ^ ¬p)) + (¬¬¬q → r)). Give its complexity c(4) and list all of its subformulas (without repetition). How many distinct subformulas are there? (b) Use structural induction on the complexity of formula y to show that the number of occurrences of the symbol A in p is less than or equal to the number of left brackets in y.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. (a) Sketch the construction tree of the following propositional formula y -((¬r V (r A-p)) + (¬¬¬q → r)). Give its complexity c(y) and list all of its subformulas (without repetition). How many distinct subformulas are there? (b) Use structural induction on the complexity of formula y to show that the number of occurrences of the symbol A in y is less than or equal to the number of left brackets in p.
Transcribed Image Text:1. (a) Sketch the construction tree of the following propositional formula y -((¬r V (r A-p)) + (¬¬¬q → r)). Give its complexity c(y) and list all of its subformulas (without repetition). How many distinct subformulas are there? (b) Use structural induction on the complexity of formula y to show that the number of occurrences of the symbol A in y is less than or equal to the number of left brackets in p.
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