TRUE if some but not all elements are NA

This cant be too hard, but I'm stuck.

x1 <- c(1, 1, 1, 2)
x2 <- c(NA, NA, 1, 2, 3)
x3 <- c(NA, NA, NA)

I have three possible vectors. They can either have no NAs (x1), some NAs (x2) or only NAs (x3). I want an operation to be performed only when there are some NAs but not when there are only NAs.

How do I write the condition that returns TRUE only if some of the elements are NA (but FALSE when all or none of them are NA).

Desired output

• x1 FALSE
• x2 TRUE
• x3 FALSE