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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.
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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.