FDD construction

Question

From paper 2019.02.13 Problem 2(a)

How did we go from (!b & c ^c ) to (b&c)?
Since and binds stronger than XOR.

I solved it as (!b & c ^c ) (distribution) -> (!b & c) ^ (!b&c) -> 0. T^T or F^F = 0

Answer 1

    !b&c xor c 
    = (c ? !b&1 xor 1 : !b&0 xor 0)
    = (c ? !b xor 1 : 0 xor 0)
    = (c ? b : 0)
    = b&c