How I can select rows from a dataframe that do not match?

I'm trying to identify the values in a data frame that do not match, but can't figure out how to do this.

# make data frame 
a <- data.frame( x =  c(1,2,3,4)) 
b <- data.frame( y =  c(1,2,3,4,5,6))

# select only values from b that are not in 'a'
# attempt 1: 
results1 <- b$y[ !a$x ]

# attempt 2:  
results2 <- b[b$y != a$x,]

If a = c(1,2,3) this works, as a is a multiple of b. However, I'm trying to just select all the values from data frame y, that are not in x, and don't understand what function to use.