When is a 1-in-3 SAT clause satisfied?

Question

How does exactly 1 in 3 sat work given the variables Xi, Xy, Xz if one of the variables in the formula are negative. We know that the results are if they are all positive given that: R(Xi, Xy, Xz) = TFF FTF FFT

How would the result look like if one or two of the variables were negative? R(-Xi, Xy, Xz) or R(-Xi, Xy, -Xz)

Answer 1

A 1-in-3 clause consists of three literals. It is satisfied if exactly one of these literals is true. For example, if the three literals are $\bar{x}_1,x_2,x_3$, then the three truth assignments (for $x_1,x_2,x_3$) which satisfy the clause are $(F,F,F)$, $(T,T,F)$, $(T,F,T)$.