Pic1 is question i need help with regarding with splitting algorithm. pic2 is an example of splitting algorithm. thank you

(a) AA(BVC) = (AAB) V(AAC) (b) AVB=-(-A1-B) (c) A + B = (AVB)^(AV-B) (d) A+1=-4 (e) A + B = -(AX-B) Recalling that A, = A2 iff-(A + A2) is unsatisfiable, now prove the first three equivalences above ((a) through (c)) using the splitting algorithm in the lecture slides on satisfiability. Choose the next variable and value to split on as you please. You do not need to write a trace of the algorithm. Instead, simply report the full search tree as the one on slide 18. However, number each node in the tree and show separately for each non-root node how the formula there was obtained by one or more applications of the rewrite rules of on the slides. The rules are reported below for your convenience. As in the previous problem, apply one rewrite step at a time and show all the rewrite steps. 1. -T=1 2.1. TAA = A 2.2. = 3.1. TVA T 3.2. AVTT 4. ATT 5. TA = A 6.1. A T => A 6.2. THA A 8. IT 9.1. IAA = 1 9.2. AAL => 1 10.1. IVA >> A 10.2. AVI A 11. A +1 A 1+ A = T 13. A1 = -A 14. IHA A 12. Splitting algorithm, example -((p q) ^ ( 49 ) (p+1)) 9=1 q=0 (1 +- d) +--- -((p + r) + ( pr)) P=0 =1 -Gp -p) T T The formula is unsatisfiable