2019 Feb Problem 1 a

Covert the formula to fdd (a ∨ ¬b) ∧ c. I tried to approach fdd coversion like below

1) a&c ⊕ c ⊕ b&c

On writing in RMNF I got the following

= a&!b&c ⊕ !a&!b&c ⊕ !a&b&c

= a&c ⊕ c ⊕ a&b&c ⊕ a&b

Complete DNF

a&!b&c ⊕ !a&!b&c ⊕ a&b&c ⊕ a&b&c

on performing davio decompostion where a=0 b=1 its leading to node 0 which varies from the solution given.

Please help me to optimally solve the question