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Recursive Definitions in Logic: Language and Propositional Calculus, Summaries of Constitutional Law

Recursive definitions for the language l that contains words with twice as many a's as b's, and the propositional calculus with symbols ˄, ˅, , and ¬. The definitions are given through rules, starting with an empty word in the language and the symbol c in the propositional calculus.

Typology: Summaries

2018/2019

Uploaded on 10/16/2019

can-guendogan
can-guendogan 🇹🇷

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Question -1:
={a,b} is given. L is the langauge of all words that contain twice as many a’s as
b’s. Empty word is in L. Dene L recursively.
Rule-1: L.
Rule-2.1: if L then aabb and abba and baab and bbaa L.
Rule-2.2: if aabb and abba L then abbaabba and baabbbaa L.
Question-2:
Write out the full recursive denition for the propositional calculus.
Assume that it contains symbols ˄, ˅, , ¬.
This is Question 14 (on page 29) in the textbook
Rule -1: C.
Rule-2.1: if C then ˄ and ˅ C.
Rule-2.2:if ˄ and ˅ C then and ¬ C.

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Question -1: ={a,b} is given. L is the langauge of all words that contain twice as many a’s as b’s. Empty word is in L. Define L recursively.

Rule-1: L. Rule-2.1: if L then aabb and abba and baab and bbaa L. Rule-2.2: if aabb and abba L then abbaabba and baabbbaa L. Question-2: Write out the full recursive definition for the propositional calculus. Assume that it contains symbols ˄, ˅, , ¬. This is Question 14 (on page 29) in the textbook

Rule -1: C. Rule-2.1: if C then ˄ and ˅ C. Rule-2.2:if ˄ and ˅ C then and ¬ C.