Input X contains 3 categorical features— X1, X2, X3. The joint distribution becomes:

P(X | Y) = P(X1 | Y) * P(X2 | X1, Y) * P(X3 | X1, X2, Y)

P(x1 ^ x2 ^ x3 | y) = P(x1 | y) * P(x2 | y ^ x1) * P(x3 | y ^ x1 ^ x2)

= P(x1 | y) * P(x2 | y ) * P(x3 | y ^ x2)

1) What is the caret symbol above means

2) How was the last equation derived from the one above?