Question 1: Well-formed Parenthetical Expressions) A Well-formed Parenthetical Expres- sion (WFPE) is a string over the alphabet {(, ) } that follows the usual parentheses pairing rules used in English and mathematics. The size of the WFPE is the number of (s. Some examples and non- examples: ((00))()) is a WFPE, but (O()) (() is not. ()() is a WFPE, but )()( is not. Here are all the WFPEs of size three: (0, (9)0, 0(0), ((0)), (90). For each n > 1, how many WFPEs are there of size n? (Hint: Try a bijective proof.)Question 1: Well-formed Parenthetical Expressions) A Well-formed Parenthetical Expres- sion (WFPE) is a string over the alphabet {(, ) } that follows the usual parentheses pairing rules used in English and mathematics. The size of the WFPE is the number of (s. Some examples and non- examples: ((00))()) is a WFPE, but (O()) (() is not. ()() is a WFPE, but )()( is not. Here are all the WFPEs of size three: (0, (9)0, 0(0), ((0)), (90). For each n > 1, how many WFPEs are there of size n? (Hint: Try a bijective proof.)