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How it works...
The na.omit() function internally uses the is.na() function, that allows us to find whether its argument is NA. When applied to a single value, it returns a Boolean value. When applied to a collection, it returns a vector:
> is.na(dat[4,2])
[1] TRUE
> is.na(dat$Income)
[1] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE
[10] FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
[19] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE