Create variable (dummy) depending on values of two other columns in R

Question

I would like to create a dummy that assumes 1 if A==1 and 0 if B==1. Note that A and B are dummies but with NA instead of 0. I also have observations for which neither A or B assumes value 1 and want to exclude them (rows with NAs in both columns)

structure(list(id = 1:11, A = c(1L, NA, 1L, NA, 1L, 1L, NA, 1L, 
NA, NA, NA), B = c(NA, 1L, NA, 1L, NA, NA, NA, NA, NA, NA, 1L
)), class = "data.frame", row.names = c(NA, -11L))

   id  A  B
1   1  1 NA
2   2 NA  1
3   3  1 NA
4   4 NA  1
5   5  1 NA
6   6  1 NA
7   7 NA NA
8   8  1 NA
9   9 NA NA
10 10 NA NA
11 11 NA  1