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Explaining syntactically legal boolean expression

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Q1) In this problem, we consider a very restricted subset of Boolean expressions. Define an operator to be one of  the four symbols: ¬, ∧, ∨, and →. Define a variable to be one of the five symbols: P, Q, R, S and T. Let L =  {w : w is a syntactically legal Boolean expression without parentheses and the number of operators in w is  exactly equal to the number of variables in w}. Examples:

¬P → Q is in L.
P ∧ R ∧ ¬S → R is in L.
P → Q is not in L.
¬ ¬P is not in L.
Is L regular? Prove your answer.

Reference no: EM1357483

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